DSCI 2710 PRACTICE EXAM 2-A 1. One of the following statements is false and the other four are true. Identify the false statement. a. For two events, A and B, P(A and B) is equal to P(A)AP(B) provided A and B are independent. (*) b. If P(A|B) = P(A) then events A and B are mutually exclusive. no, they are independent c. For any two events, A and B, P(A and B) is less than or equal to P(A). d. For two events, A and B, P(A or B) is equal to P(A) + P(B) provided A and B are mutually exclusive. e. For any two events, A and B, P(A or B) is greater than or equal to P(A). 2. One of the following statements is false and the other four are true. Identify the false statement. a. In a binomial situation, the trials are independent. (*) b. When selecting items without replacement, the trials are independent. must be with replacement c. The number of heads in n flips of an unfair coin (probability of flipping a head each time is not ) is an example of a binomial random variable. d. Twenty components are selected with replacement from a batch of components, where each component is either defective or not defective. The number of defective components (out of 20) would be a binomial random variable. e. If the average arrival rate is five per hour for a Poisson process, the mean of the random variable X = number of arrivals over any 2-hour period is found by simply doubling the value of five; that is = 10. 3. If two events A and B are such that they cannot both occur, they are said to be ___________________. a. marginal events b. rare events c. mutually dependent d. independent (*) e. mutually exclusive Problems 4 - 8 use the following information. A mail-order firm keeps track of the orders it receives from three geographical regions, East, West, and North. For each region, the number of customers ordering size small, size medium, and size large was observed. The data are shown below. One of the orders is selected at random. SIZE REGION East (E) West (W) North (N) TOTAL Small (S) 100 60 90 250 Medium (M) 160 140 100 400 Large (L) TOTAL 140 400 150 350 60 250 350 1000 4. What is the probability that the order is from the West region? This is P(W). a. .06 b. .25 (*) c. .35 350/1000 d. .45 e. .30 5. What is P(W or S)? This represents the chances that the selected order is from the West region or is for the small size. a. .06 b. .45 (*) c. .54 (350 + 100 + 90)/1000 d. .60 e. .72 6. What is P(E*S)? a. .10 (*) b. .40 100/250 c. .35 d. .25 e. .20 7. Are events M and E independent? a. Yes, since P(M and E) is zero. (*) b. Yes, since P(M*E) is the same as P(M). P(M|E) = 160/400 = .4 = P(M) c. Yes, since P(M*E) is the same as P(E). d. No, since P(M*E) is not the same as P(M). e. No, since P(M and E) is not zero. 8. Are events M and E mutually exclusive? a. Yes, since P(M and E) is zero. b. Yes, since P(M*E) is the same as P(M). c. Yes, since P(M*E) is the same as P(E). d. No, since P(M*E) is not the same as P(M). (*) e. No, since P(M and E) is not zero. Problems 9 and 10 use the following information. A certain plant contains 40% male workers and 60% female workers. Also, 30% of the workers have a college degree. In addition, 20% of the female workers have a college degree. 9. What proportion of the workers are female or have a college degree? a. .36 b. .12 male female (*) c. .78 degree 18 12 30 d. .90 no degree 22 48 70 e. .64 40 60 100 10. What percentage of the male workers have a college degree? (*) a. 45% 18/40 b. 60% c. 18% d. 75% e. 12% Problems 11 - 14 use the following information. Consider the following discrete random variable. 1 X= 2 3 4 with probability .5 with probability .3 with probability .1 with probability .1 11. What is the probability that X is no more than 3? a. .1 b. .5 c. .2 d. .8 (*) e. .9 P(X # 3) = .5 + .3 + .1 12. What is the probability that the absolute value of (X - 2.5) is at least 1? a. .3 (*) b. .6 |X - 2.5| > 1 only if X = 1 or X = 4. This probability is .5 + .1. c. .2 d. .5 e. .4 13. What is the mean of X? a. 2.5 b. 3 c. 1.5 d. 2.75 (*) e. 1.8 14. What is the standard deviation of X? a. 1.12 b. 0.76 (*) c. 0.98 d. 1.07 e. 0.62 Problems 15 - 18 use the following information. A particular group of produced parts contains 30% that are defective. A sample of 15 parts is obtained, with replacement Let X be the number of defective parts in the sample. 15. What is the probability P(4 # X # 6)? (*) a. .572 use Table A.1 b. .206 c. .613 d. .484 e. .752 16. What is the probability that X is no more than two? a. .872 b. .092 (*) c. .127 use Table A.2 to find P(X # 2) d. .964 e. .662 17. What is the mean of X? a. 5.0 b. 7.5 c. 6.0 (*) d. 4.5 (15)(.3) e. 6.5 18. What is the standard deviation of X? a. 2.11 b. 3.15 c. 2.93 d. 2.58 (*) e. 1.77 square root of (15)(.3)(.7) Problems 19 - 22 use the following information. A media consultant carried out a survey of reading habits of CFO's. It was found that 15% of them read the Wall Street Journal before coming to work each day. Suppose a random sample of 10 CFO's is obtained. 19. What is the probability that no more than two read the Wall Street Journal before coming to work each day? a. .950 b. .130 c. .544 (*) d. .820 use the PMF to find P(X # 2) = P(0) + P(1) + P(2) e. .456 20. What is the probability that exactly one CFO reads the Wall Street Journal before coming to work each day? (*) a. .347 use the PMF to find P(1) = 10C1(.15)1(.85)9 b. .413 c. .388 d. .279 e. .216 21. For a sample size of 10, what is the mean of X, where X is the number of CFO's who read the Wall Street Journal before coming to work each day? a. 1.0 b. 1.75 (*) c. 1.5 (10)(.15) d. 2.05 e. 2.15 22. Referring to problem 21, what is the standard deviation of X? a. 0.872 b. 1.458 (*) c. 1.129 square root of (10)(.15)(.85) d. 2.063 e. 1.805 23. When flipping a coin 10 times, how many ways can you get 7 heads and 3 tails? a. 230 b. 185 c. 380 (*) d. 120 10C7 e. 290 Problems 24 and 25 use the following information. At Case Manufacturing, 60% of the units produced are produced during the day shift and the remaining 40% during the night shift. It is estimated that 10% of all units produced are defective. In addition, 5% of the units produced during the day shift are defective. 24. What is the probability that a randomly selected unit is defective and is produced during the day shift? (*) a. b. c. d. e. .03 .15 .11 .05 .08 day defective 3 not defective 57 60 night 7 10 33 90 40 100 25. What percentage of the night shift units are defective? a. 25% b. 7% c. 70% d. 30.5% (*) e. 17.5% 7/40 DSCI 2710 PRACTICE EXAM 2-B 1. The probability of selecting a customer who is female and married out of a group of customers in a department store is an example of a _______ probability whereas the probability of selecting a customer who is married given that the customer is a female is an example of a ____________ probability. a. marginal, joint b. conditional, marginal (*) c. joint, conditional d. conditional, joint e. joint, marginal In problem 2, four of the statements are true and one is false. Which statement is false? 2. a. A situation with n independent trials, where X = the number of successes in the n trials, describes a binomial situation. b. In a binomial situation, there must be only two possible outcomes for each trial. c. For any Poisson random variable, P(X # 2) is always greater than or equal to P(X < 2). d. The variance of a discrete random variable is never negative, (*) e. The mean of any discrete random variable is = np. must be binomial 3. The probability P(A or B) is equal to P(A) + P(B) provided A and B are _____________ and the probability P(A and B) is equal to P(A) A P(B) provided A and B are ______________. a. independent, mutually exclusive b. not independent, not mutually exclusive (*) c. mutually exclusive, independent d. not mutually exclusive, not independent e. independent, not mutually exclusive Problems 4 - 8 use the following information. Employees of Case Services are divided among three divisions: Management and administration, machine operations, and maintenance. The following table shows the number of employees in each division, classified by gender. One employee is randomly selected. Mgt. and administration Machine operators Maintenance Total Female 20 75 5 Male 10 125 15 Total 30 200 20 100 150 250 4. What is the probability that this employee is a female or is a machine operator? a. .80 b. .08 c. .30 (*) d. .90 (200 + 20 + 5)/250 e. .75 5. If it is known that a male was selected, what is the probability that this person is not in the maintenance division? a. .95 b. .75 c. .67 d. .83 (*) e. .90 (10 + 125)/150 6. What is the probability of selecting a female from the group of maintenance workers? (*) a. .25 5/20 b. .33 c. .02 d. .05 e. .15 7. Are the events Male and Maintenance independent? a. Yes, since P(Male | Maintenance) is equal to P(Male) b. Yes, since P(Male and Maintenance) is equal to zero c. Yes, since P(Male or Maintenance) = P(Male) A P(Maintenance) (*) d. No, since P(Male | Maintenance) is not equal to P(Male) e. No, since P(Male and Maintenance) is not equal to zero 8. Are the events Male and Maintenance mutually exclusive? a. Yes, since P(Male | Maintenance) is equal to P(Male) b. Yes, since P(Male and Maintenance) is equal to zero c. Yes, since P(Male or Maintenance) = P(Male) A P(Maintenance) d. No, since P(Male | Maintenance) is not equal to P(Male) (*) e. No, since P(Male and Maintenance) is not equal to zero Problems 9 and 10 use the following information. At Allied Manufacturing, 60% of the units produced are produced during the day shift and the remaining 40% during the night shift. It is estimated that 10% of all units produced are defective. In addition, 5% of the units produced during the day shift are defective. 9. What is the probability that a randomly selected unit is defective and is produced during the day shift? a. .050 (*) b. .030 day night c. .048 defective 3 7 10 d. .020 not defective 57 33 90 e. .015 60 40 100 10. What percentage of the night shift units are defective? a. 8.5% b. 19% (*) c. 17.5% 7/40 d. 22% e. 30% Problems 11 - 14 use the following information. The random variable X has the following probability distribution. 1 with prob. .1 2 with prob. .2 X = 3 with prob. .2 4 with prob. .2 5 with prob. .3 11. What is the probability that X is at least 3? a. .2 b. .3 c. .5 (*) d. .7 P(X $ 3) = .2 + .2 + .3 e. .9 12. What is the probability that X is no more than 2? a. .2 b. .5 c. .7 (*) d. .3 P(X # 2) = .1 + .2 e. .9 13. What is the mean of X? (*) a. 3.4 b. 3.7 c. 2.1 d. 2.6 e. 3.0 14. What is the standard deviation of X? a. 1.77 b. 2.01 c. 1.18 (*) d. 1.36 e. 2.29 Problems 15 - 17 use the following information. The number of accidents per month at Allied Manufacturing follows a Poisson distribution with an average of 3.5 accidents per month. Let X = the number of accidents during a particular month. 15. What is the probability of observing 4 accidents (that is, X = 4)? a. .158 (*) b. .189 Use Table A.3 c. .083 d. .216 e. .134 16. What is the standard deviation of X? (*) a. 1.87 square root of 3.5 b. 2.16 c. 2.50 d. 2.81 e. 1.58 17. What is the probability of observing 8 accidents over a two-month period? a. .1872 b. .0169 c. .0338 (*) d. .1304 Use Table 8.3 with mu = 7 e. .2107 Problems 18 - 22 use the following information. Thirty percent of the time, a purchaser of a Case Manufacturing product also purchases an extended warranty. A sample of 15 Case Manufacturing purchases is obtained. Let X represent the number of purchases for which an extended warranty was also purchased. 18. What is the probability that X is 3? a. .186 (*) b. .170 use Table A.1 with n = 15 and p = .3 c. .217 d. .282 e. .161 19. What is the probability that X is at least 2? a. .128 b. .986 (*) c. .965 use Table A.2 and find 1 - P(X # 1) = 1 - .035 d. .873 e. .092 20. What is the probability X is no more than 5? a. .485 (*) b. .722 use Table A.2 and find P(X # 5) c. .206 d. .869 e. .278 21. What is the mean of X? a. 7.5 b. 2.2 c. 3.1 d. 3.6 (*) e. 4.5 (15)(.3) 22. What is the standard deviation of X? a. 2.16 (*) b. 1.77 square root of (15)(.3)(.7) c. 1.59 d. 2.53 e. 2.92 Problems 23 - 25 use the following information. At a particular web site, 25% of the people who visit this site make a purchase. Let X be the number of people in the next group of 12 web site visitors who make a purchase. 23. What is the probability that exactly four people will make a purchase? a. .156 (*) b. .194 use the PMF to find 12C4(.25)4(.75)8 c. .203 d. .176 e. .221 24. Determine the probability that X is no more than one. a. .127 b. .841 c. .116 (*) d. .158 use the PMF to find P(X # 1) = P(0) + P(1) e. .968 25. If X is observed indefinitely, the average number of site visitors (out of 12) who make a purchase is _______. a. 5 b. 7.5 (*) c. 3.0 (12)(.25) d. 2.5 e. 4.25 DSCI 2710 PRACTICE EXAM 2-C 1. Four of the following five statements are false. Which statement is true? a. The mean of any discrete random variable is = np. b. The variance of a random variable can occasionally be negative. (*) c. For a binomial random variable, the trials must be independent. d. P(A|B) is never the same as P(A). e. If X is a binomial random variable, then all values of X are equally likely to occur. 2. If two events A and B are such that they cannot both occur, they are said to be ___________________. a. mutually dependent b. independent (*) c. mutually exclusive d. marginal events e. rare events 3. You can add \"OR\" probabilities provided the events are _______________ and you can multiply \"AND\" probabilities provided the events are _______________. a. independent, mutually exclusive b. not related, dependent c. marginal, independent d. mutually exclusive, marginal (*) e. mutually exclusive, independent Problems 4 through 7 use the following information. A group of 500 students is categorized by their major (FINA, MKTG, ITDS, ACCT) and how they arrive at their classes (W = walk, D = drive, B = bus). A student is picked at random from this group of 500. W D B Total MKTG 25 20 35 FINA 60 60 40 ITDS 30 70 10 ACCT 60 50 40 80 160 110 150 Total 175 200 125 500 4. What is P(FINA)? a. .22 (*) b. .32 160/500 c. .48 d. .16 e. .12 5. What proportion of the marketing majors (MKTG) walk to their classes? a. .14 b. .20 (*) c. .31 25/80 d. .55 e. .25 6. What is P(FINA*B)? (*) a. .32 40/125 b. .12 c. .25 d. .30 e. .40 7. Are the events D and ITDS mutually exclusive? a. Yes, since P(D or ITDS) = P(D) A P(ITDS) b. No, since P(D | ITDS) is not equal to P(D) (*) c. No, since P(D and ITDS) is not equal to zero d. Yes, since P(D | ITDS) is equal to P(D) e. Yes, since P(D and ITDS) is equal to zero Problems 8 through 11 use the following information. A certain plant contains 40% male workers and 60% female workers. Also, 30% of the workers have a college degree. In addition, 50% of those with a college degree are males. 8. What proportion of the workers are male and have a college degree? a. .55 b. .12 male female (*) c. .15 degree 15 15 30 45 70 d. .37 no degree 25 e. .06 40 60 100 9. If a female worker is selected at random, what is the probability that this person has a college degree. a. .15 b. .50 c. .45 (*) d. .25 15/60 e. .20 10. Are the events \"male\" and \"college degree\" independent? a. No, since P(college degree | male) is not equal to P(male) (*) b. No, since P(college degree | male) is not equal to P(college degree) c. No, since P(college degree and male) is not equal to zero d. Yes, since P(college degree | male) is equal to P(college degree) e. Yes, since P(college degree and male) is equal to zero 11. Are the events \"male\" and \"college degree\" mutually exclusive? a. No, since P(college degree | male) is not equal to P(male) b. No, since P(college degree | male) is not equal to P(college degree) (*) c. No, since P(college degree and male) is not equal to zero d. Yes, since P(college degree | male) is equal to P(college degree) e. Yes, since P(college degree and male) is equal to zero Problems 12through 14 use the following information. The random variable X has the following probability distribution. X= 1 2 3 4 5 with prob. .1 with prob. .1 with prob. .3 with prob. .3 with prob. .2 12. What is the probability that X is less than 4? a. .8 b. .3 c. .6 (*) d. .5 P(X < 4) = P(X # 3) = .1 + .1 + .3 e. .7 13. What is the mean of X? a. 2.4 b. 3.0 c. 2.8 d. 4.2 (*) e. 3.4 14. What is the standard deviation of X? a. 3.79 b. 2.24 c. 1.44 d. 2.86 (*) e. 1.20 Problems 15 through 17 use the following information. In Burnsville, 65% of the people subscribe to the local newspaper. A random sample of 18 subscribers is obtained. Let X be the number of people (out of the 18) who subscribe to the local newspaper. 15. What is the probability that exactly twelve people subscribe to the local newspaper? a. .155 b. .312 c. .108 d. .226 (*) e. .194 use the PMF to find 18C12(.65)12(.35)6 16. Determine the probability that X is at least 17. a. .0258 b. .0031 c. .0127 (*) d. .0046 use the PMF to find P(17) + P(18) e. .0193 17. If X is observed indefinitely, the average number of people (out of 18) who subscribe to the local newspaper is _______. a. 12.8 b. 8.2 c. 9.0 (*) d. 11.7 This is the mean of X and is equal to np = (18)(.65) e. 6.67 Problems 18 through 22 use the following information. Accident claims are checked for completeness by a branch office before they are sent to the regional office for payment. Suppose that the probability that a claim is complete is .4. Consider a sample of 12 claims and let represent the number of claims that are complete (out of 12). 18. What is the probability that exactly 4 of the claims are complete? a. .289 b. .318 c. .363 d. .236 (*) e. .213 use Table A.1 19. What is the probability that at least 5 of the claims are complete. a. .334 b. .438 c. .227 (*) d. .562 use Table A.2 to find 1 - P(X # 4) = 1 - .438 e. .665 20. What is the probability that no more than 2 of the claims are complete? a. .064 b. .981 (*) c. .083 use Table A.2 to find P(X # 2) d. .225 e. .917 21. What is the mean of X? a. 3.6 b. 3.1 c. 2.5 d. 4.1 (*) e. 4.8 This is np = (12)(.4) 22. What is the standard deviation of X? a. 2.07 b. 1.59 c. 2.88 d. 2.52 (*) e. 1.70 This is the square root of np(1 - p) Problems 23 thru 25 use the following information. Allied Taxi Service has studied the demand for taxis at the local airport and found that on average 5 taxis are demanded per hour. It is assumed that the taxi demand per hour follows a Poisson distribution. Let X represent the number of arrivals over a one-hour period. 23. What is the probability that the taxi demand is less than 3 during a particular hour? a. .177 (*) b. .125 use Table A.3 to find P(X < 3) = P(0) + P(1) + P(2) c. .131 d. .383 e. .276 24. The standard deviation of X is __________. a. 1.33 b. 2.50 c. 1.75 (*) d. 2.24 this is the square root of the variance = square root of the mean (5) e. 3.12 25. Over a particular two-hour period, what is the probability that the taxi demand is exactly 6 taxis? a. .146 (*) b. .063 use mu = 10 in Table A.3 and find P(6) c. .174 d. .212 e. .165 DSCI 2710 PRACTICE EXAM 3 - D In problem 1, four statements are true and one is false. Which statement is false? 1. a. For a continuous random variable (X) a probability can be specified for an interval, such as P(X > 6), but is not meaningful for an exact value of the variable, such as, for example, P(X = 6). (*) b. For a normally distributed random variable, the probability that it takes on values greater than zero is always 0.5. no, not unless the mean is zero (like the Z curve). If this were true, then half the male heights would be negative. I know that I'm short but my height is not a negative number! c. For the standard normal distribution, P(Z = 0) is equal to zero. d. Not all the probability distributions for continuous random variables are normal. e. The area under a normal curve between two points, a and b, represents the probability that the normal variable, X, takes on values between a and b. 2. The Central Limit Theorem states that when obtaining a large sample (generally, n > ____) from any population, the sample mean will follow an approximate _______ distribution. a. 40, Student's t (*) b. 30, normal c. 50, uniform d. 50, normal e. 30, uniform 3. A Z-score (value) of -1.8 indicates that the value of the variable X is __________ standard deviations to the _________ of the mean. a. 3.6 variances, left b. 1.8 standard deviations, right c. 1.8 variances, left (*) d. 1.8 standard deviations, left e. 3.6 variances, right For problems 4 thru 8, Z represents the standard normal random variable. 4. Find P(-1.3 # Z # 1.5) a. .0300 b. .9579 (*) c. .8364 .4332 + .4032 d. .0297 e. .7726 5. Find P(Z $ 1.83) a. .4641 b. .4664 c. .9664 d. .9641 (*) e. .0336 6. Find the probability that Z is at least 1 a. .8413 b. .2786 (*) c. .1587 this is P(Z > 1) d. .7214 e. .3413 7. Find the value of Z (say, z) such that P(Z $ z) = .8 a. .52 (*) b. -.84 DRAW THE PICTURE! The area to the right of z is .8. So, z = -.84. c. -1.24 d. -.52 e. .84 8. Find the value of Z (say, z) such that P(Z # z) = .65 (*) a. .39 same suggestion. The area to the left of z is .65. So, z = .39. b. 1.04 c. .77 d. -.39 e. -1.04 Problems 9 thru 15 use the following information. The time spent by airplanes in the repair facility (X) of a particular airlines is believed to follow a normal distribution with mean 13.2 hours and standard deviation 3.5 hours. 9. What proportion of the planes spend more than 17 hours in the repair facility? a. .2144 (*) b. .1379 same as P(Z > 1.09) c. .4767 d. .9767 e. .8621 10. Eighty percent of the planes spend no more than _________ hours in the repair facility. (*) a. 16.14 area to left of Z is .8. So, Z = .84 and (x - 13.2)/3.5 = .84. Solve for x. b. 11.38 c. 10.26 d. 17.66 e. 15.02 11. Fifty percent of the planes spend at least how many hours in the repair facility? a. 11.87 b. 15.16 (*) c. 13.2 that would have to be the mean of 13.2 hours (area to the right of the mean = .5) d. 16.35 e. 14.67 12 Consider a random sample of size 25. The sample mean ( X ) is a random variable with a mean of ______ hours. (*) a. 13.2 this would be mu = 13.2 b. 13.2/5 = 2.64 c. 13.2/25 = .53 d. (13.2)(25) = 330 e. 13.2 + 3.5 = 16.7 13 Consider a random sample of size 25. The sample mean ( X ) is a random variable with a standard deviation of _______ hours. a. 1.5 b. 3.5 c. .14 d. 2.1 (*) e. .7 this is 3.5/sqrt(25) 14 Consider a random sample of size 25. What is the probability that the sample mean ( X ) is more than 14.5 hours? a. .0628 b. .2173 c. .3557 (*) d. .0314 this is P(Z > (14.5 - 13.2)/.7) = P(Z > 1.86) e. .0529 15. Consider a random sample of size 25. What is the probability that the sample mean ( X ) is between 13 hours and 14 hours? a. .1380 (*) b. .4870 this is P(-.29 < Z < 1.14) = .1141 + .3729 c. .3162 d. .2588 e. .3971 Problems 16 - 20 use the following information. The length of time it takes Glenda to drive home (say, X) follows a normal distribution with a mean of 45 minutes and a standard deviation of 15 minutes. 16. What is P(X > 60 minutes)? (*) a. .1587 same as P(Z > 1) b. .7734 c. .3413 d. .8413 e. .2266 17. Ninety percent of the time Glenda's driving time is less than _______ minutes. a. 25.8 b. 70.6 (*) c. 64.2 Z value with an area to the left of .9 is Z = 1.28. So, (x - 45)/15 = 1.28. d. 19.4 e. 68.4 18. What fraction of time is Glenda's driving time less than 20 minutes? (*) a. .0475 same as P(Z < -1.67) b. .1056 c. .9525 d. .1587 e. .8944 19. Find P(X < 45 minutes). a. 1.0 b. .25 c. .75 (*) d. .50 the area to the left of the mean is always .5 e. 0 20. Twenty percent of the driving times for Glenda are less than what amount? a. 41.3 minutes b. 61.8 minutes (*) c. 32.4 minutes Z value with a left-tail area of .2 is Z = -.84. So, (x - 45)/15 = -.84. d. 28.2 minutes e. 57.6 minutes 3336-CDAppA.pdf Appendix A 1/6/05 5:37 PM Page 2 Tables APPENDIX A TABLE A.1 TABLES Binomial probabilities [nCxpx(1 - p)n-x]. P 2 n 2 x 0 1 2 0.01 .980 .020 .000 0.05 .902 .095 .003 0.10 .810 .180 .010 0.20 .640 .320 .040 0.30 .490 .420 .090 0.40 .360 .480 .160 0.50 .250 .500 .250 0.60 .160 .480 .360 0.70 .090 .420 .490 0.80 .040 .320 .640 0.90 .010 .180 .810 0.95 .003 .095 .902 0.99 .000 .020 .980 x 0 1 2 3 0 1 2 3 .970 .029 .000 .000 .857 .135 .007 .000 .729 .243 .027 .001 .512 .384 .096 .008 .343 .441 .189 .027 .216 .432 .288 .064 .125 .375 .375 .125 .064 .288 .432 .216 .027 .189 .441 .343 .008 .096 .384 .512 .001 .027 .243 .729 .000 .007 .135 .857 .000 .000 .029 .970 0 1 2 3 4 0 1 2 3 4 .961 .039 .001 .000 .000 .815 .171 .014 .000 .000 .656 .292 .049 .004 .000 .410 .410 .154 .026 .002 .240 .412 .265 .076 .008 .130 .346 .346 .154 .026 .063 .250 .375 .250 .063 .026 .154 .346 .346 .130 .008 .076 .265 .412 .240 .002 .026 .154 .410 .410 .000 .004 .049 .292 .656 .000 .000 .014 .171 .815 .000 .000 .001 .039 .961 0 1 2 3 4 5 0 1 2 3 4 5 .951 .048 .001 .000 .000 .000 .774 .204 .021 .001 .000 .000 .590 .328 .073 .008 .000 .000 .328 .410 .205 .051 .006 .000 .168 .360 .309 .132 .028 .002 .078 .259 .346 .230 .077 .010 .031 .156 .312 .312 .156 .031 .010 .077 .230 .346 .259 .078 .002 .028 .132 .309 .360 .168 .000 .006 .051 .205 .410 .328 .000 .000 .008 .073 .328 .590 .000 .000 .001 .021 .204 .774 .000 .000 .000 .001 .048 .951 0 1 2 3 4 5 6 0 1 2 3 4 5 6 .941 .057 .001 .000 .000 .000 .000 .735 .232 .031 .002 .000 .000 .000 .531 .354 .098 .015 .001 .000 .000 .262 .393 .246 .082 .015 .002 .000 .118 .303 .324 .185 .060 .010 .001 .047 .187 .311 .276 .138 .037 .004 .016 .094 .234 .313 .234 .094 .016 .004 .037 .138 .276 .311 .187 .047 .001 .010 .060 .185 .324 .303 .118 .000 .002 .015 .082 .246 .393 .262 .000 .000 .001 .015 .098 .354 .531 .000 .000 .000 .002 .031 .232 .735 .000 .000 .000 .000 .001 .057 .941 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 .932 .066 .002 .000 .000 .000 .000 .000 .698 .257 .041 .004 .000 .000 .000 .000 .478 .372 .124 .023 .003 .000 .000 .000 .210 .367 .275 .115 .029 .004 .000 .000 .082 .247 .318 .227 .097 .025 .004 .000 .028 .131 .261 .290 .194 .077 .017 .002 .008 .055 .164 .273 .273 .164 .055 .008 .002 .017 .077 .194 .290 .261 .131 .028 .000 .004 .025 .097 .227 .318 .247 .082 .000 .000 .004 .029 .115 .275 .367 .210 .000 .000 .000 .003 .023 .124 .372 .478 .000 .000 .000 .000 .004 .041 .257 .698 .000 .000 .000 .000 .000 .002 .066 .932 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 .923 .075 .003 .000 .000 .000 .000 .000 .000 .663 .279 .051 .005 .000 .000 .000 .000 .000 .430 .383 .149 .033 .005 .000 .000 .000 .000 .168 .336 .294 .147 .046 .009 .001 .000 .000 .058 .198 .296 .254 .136 .047 .010 .001 .000 .017 .090 .209 .279 .232 .124 .041 .008 .001 .004 .031 .109 .219 .273 .219 .109 .031 .004 .001 .008 .041 .124 .232 .279 .209 .090 .017 .000 .001 .010 .047 .136 .254 .296 .198 .058 .000 .000 .001 .009 .046 .147 .294 .336 .168 .000 .000 .000 .000 .005 .033 .149 .383 .430 .000 .000 .000 .000 .000 .005 .051 .279 .663 .000 .000 .000 .000 .000 .000 .003 .075 .923 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 .914 .083 .003 .000 .000 .000 .000 .000 .000 .000 .630 .299 .063 .008 .001 .000 .000 .000 .000 .000 .387 .387 .172 .045 .007 .001 .000 .000 .000 .000 .134 .302 .302 .176 .066 .017 .003 .000 .000 .000 .040 .156 .267 .267 .172 .074 .021 .004 .000 .000 .010 .060 .161 .251 .251 .167 .074 .021 .004 .000 .002 .018 .070 .164 .246 .246 .164 .070 .018 .002 .000 .004 .021 .074 .167 .251 .251 .161 .060 .010 .000 .000 .004 .021 .074 .172 .267 .267 .156 .040 .000 .000 .000 .003 .017 .066 .176 .302 .302 .134 .000 .000 .000 .000 .001 .007 .045 .172 .387 .387 .000 .000 .000 .000 .000 .001 .008 .063 .299 .630 .000 .000 .000 .000 .000 .000 .000 .003 .083 .914 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 .904 .091 .004 .000 .000 .000 .000 .000 .000 .000 .000 .599 .315 .075 .010 .001 .000 .000 .000 .000 .000 .000 .349 .387 .194 .057 .011 .001 .000 .000 .000 .000 .000 .107 .268 .302 .201 .088 .026 .006 .001 .000 .000 .000 .028 .121 .233 .267 .200 .103 .037 .009 .001 .000 .000 .006 .040 .121 .215 .251 .201 .111 .042 .011 .002 .000 .001 .010 .044 .117 .205 .246 .205 .117 .044 .010 .001 .000 .002 .011 .042 .111 .201 .251 .215 .121 .040 .006 .000 .000 .001 .009 .037 .103 .200 .267 .233 .121 .028 .000 .000 .000 .001 .006 .026 .088 .201 .302 .268 .107 .000 .000 .000 .000 .000 .001 .011 .057 .194 .387 .349 .000 .000 .000 .000 .000 .000 .001 .010 .075 .315 .599 .000 .000 .000 .000 .000 .000 .000 .000 .004 .091 .904 0 1 2 3 4 5 6 7 8 9 10 3336-CDAppA.pdf 1/6/05 5:37 PM Page 3 Appendix A TABLE A.1 Tables Binomial probabilities [nCxpx(1 - p)n-x] (continued). P n 11 x 0 1 2 3 4 5 6 7 8 9 10 11 0.01 .895 .099 .005 .000 .000 .000 .000 .000 .000 .000 .000 .000 0.05 .569 .329 .087 .014 .001 .000 .000 .000 .000 .000 .000 .000 0.10 .314 .384 .213 .071 .016 .002 .000 .000 .000 .000 .000 .000 0.20 .086 .236 .295 .221 .111 .039 .010 .002 .000 .000 .000 .000 0.30 .020 .093 .200 .257 .220 .132 .057 .017 .004 .001 .000 .000 0.40 .004 .027 .089 .177 .236 .221 .147 .070 .023 .005 .001 .000 0.50 .000 .005 .027 .081 .161 .226 .226 .161 .081 .027 .005 .000 0.60 .000 .001 .005 .023 .070 .147 .221 .236 .177 .089 .027 .004 0.70 .000 .000 .001 .004 .017 .057 .132 .220 .257 .200 .093 .020 0.80 .000 .000 .000 .000 .002 .010 .039 .111 .221 .295 .236 .086 0.90 .000 .000 .000 .000 .000 .000 .002 .016 .071 .213 .384 .314 0.95 .000 .000 .000 .000 .000 .000 .000 .001 .014 .087 .329 .569 0.99 .000 .000 .000 .000 .000 .000 .000 .000 .000 .005 .099 .895 x 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12 .886 .107 .006 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .540 .341 .099 .017 .002 .000 .000 .000 .000 .000 .000 .000 .000 .282 .377 .230 .085 .021 .004 .000 .000 .000 .000 .000 .000 .000 .069 .206 .283 .236 .133 .053 .016 .003 .001 .000 .000 .000 .000 .014 .071 .168 .240 .231 .158 .079 .029 .008 .001 .000 .000 .000 .002 .017 .064 .142 .213 .227 .177 .101 .042 .012 .002 .000 .000 .000 .003 .016 .054 .121 .193 .226 .193 .121 .054 .016 .003 .000 .000 .000 .002 .012 .042 .101 .177 .227 .213 .142 .064 .017 .002 .000 .000 .000 .001 .008 .029 .079 .158 .231 .240 .168 .071 .014 .000 .000 .000 .000 .001 .003 .016 .053 .133 .236 .283 .206 .069 .000 .000 .000 .000 .000 .000 .000 .004 .021 .085 .230 .377 .282 .000 .000 .000 .000 .000 .000 .000 .000 .002 .017 .099 .341 .540 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .006 .107 .886 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0 1 2 3 4 5 6 7 8 9 10 11 12 13 .878 .115 .007 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .513 .351 .111 .021 .003 .000 .000 .000 .000 .000 .000 .000 .000 .000 .254 .367 .245 .100 .028 .006 .001 .000 .000 .000 .000 .000 .000 .000 .055 .179 .268 .246 .154 .069 .023 .006 .001 .000 .000 .000 .000 .000 .010 .054 .139 .218 .234 .180 .103 .044 .014 .003 .001 .000 .000 .000 .001 .011 .045 .111 .184 .221 .197 .131 .066 .024 .006 .001 .000 .000 .000 .002 .010 .035 .087 .157 .209 .209 .157 .087 .035 .010 .002 .000 .000 .000 .001 .006 .024 .066 .131 .197 .221 .184 .111 .045 .011 .001 .000 .000 .000 .001 .003 .014 .044 .103 .180 .234 .218 .139 .054 .010 .000 .000 .000 .000 .000 .001 .006 .023 .069 .154 .246 .268 .179 .055 .000 .000 .000 .000 .000 .000 .000 .001 .006 .028 .100 .245 .367 .254 .000 .000 .000 .000 .000 .000 .000 .000 .000 .003 .021 .111 .351 .513 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .007 .115 .878 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 .869 .123 .008 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .488 .359 .123 .026 .004 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .229 .356 .257 .114 .035 .008 .001 .000 .000 .000 .000 .000 .000 .000 .000 .044 .154 .250 .250 .172 .086 .032 .009 .002 .000 .000 .000 .000 .000 .000 .007 .041 .113 .194 .229 .196 .126 .062 .023 .007 .001 .000 .000 .000 .000 .001 .007 .032 .085 .155 .207 .207 .157 .092 .041 .014 .003 .001 .000 .000 .000 .001 .006 .022 .061 .122 .183 .209 .183 .122 .061 .022 .006 .001 .000 .000 .000 .001 .003 .014 .041 .092 .157 .207 .207 .155 .085 .032 .007 .001 .000 .000 .000 .000 .001 .007 .023 .062 .126 .196 .229 .194 .113 .041 .007 .000 .000 .000 .000 .000 .000 .002 .009 .032 .086 .172 .250 .250 .154 .044 .000 .000 .000 .000 .000 .000 .000 .000 .001 .008 .035 .114 .257 .356 .229 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .004 .026 .123 .359 .488 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .008 .123 .869 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 .860 .130 .009 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .463 .366 .135 .031 .005 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .206 .343 .267 .129 .043 .010 .002 .000 .000 .000 .000 .000 .000 .000 .000 .000 .035 .132 .231 .250 .188 .103 .043 .014 .003 .001 .000 .000 .000 .000 .000 .000 .005 .031 .092 .170 .219 .206 .147 .081 .035 .012 .003 .001 .000 .000 .000 .000 .000 .005 .022 .063 .127 .186 .207 .177 .118 .061 .024 .007 .002 .000 .000 .000 .000 .000 .003 .014 .042 .092 .153 .196 .196 .153 .092 .042 .014 .003 .000 .000 .000 .000 .000 .002 .007 .024 .061 .118 .177 .207 .186 .127 .063 .022 .005 .000 .000 .000 .000 .000 .001 .003 .012 .035 .081 .147 .206 .219 .170 .092 .031 .005 .000 .000 .000 .000 .000 .000 .001 .003 .014 .043 .103 .188 .250 .231 .132 .035 .000 .000 .000 .000 .000 .000 .000 .000 .000 .002 .010 .043 .129 .267 .343 .206 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .005 .031 .135 .366 .463 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .009 .130 .860 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 3 3336-CDAppA.pdf Appendix A 1/6/05 5:37 PM Page 4 Tables TABLE A.1 Binomial probabilities [nCxpx(1 - p)n-x] (continued). P 4 n 16 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.01 .851 .138 .010 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 0.05 .440 .371 .146 .036 .006 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 0.10 .185 .329 .275 .142 .051 .014 .003 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 0.20 .028 .113 .211 .246 .200 .120 .055 .020 .006 .001 .000 .000 .000 .000 .000 .000 .000 0.30 .003 .023 .073 .146 .204 .210 .165 .101 .049 .019 .006 .001 .000 .000 .000 .000 .000 0.40 .000 .003 .015 .047 .101 .162 .198 .189 .142 .084 .039 .014 .004 .001 .000 .000 .000 0.50 .000 .000 .002 .009 .028 .067 .122 .175 .196 .175 .122 .067 .028 .009 .002 .000 .000 0.60 .000 .000 .000 .001 .004 .014 .039 .084 .142 .189 .198 .162 .101 .047 .015 .003 .000 0.70 .000 .000 .000 .000 .000 .001 .006 .019 .049 .101 .165 .210 .204 .146 .073 .023 .003 0.80 .000 .000 .000 .000 .000 .000 .000 .001 .006 .020 .055 .120 .200 .246 .211 .113 .028 0.90 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .003 .014 .051 .142 .275 .329 .185 0.95 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .006 .036 .146 .371 .440 0.99 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .010 .138 .851 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 .843 .145 .012 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .418 .374 .158 .041 .008 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .167 .315 .280 .156 .060 .017 .004 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .023 .096 .191 .239 .209 .136 .068 .027 .008 .002 .000 .000 .000 .000 .000 .000 .000 .000 .002 .017 .058 .125 .187 .208 .178 .120 .064 .028 .009 .003 .001 .000 .000 .000 .000 .000 .000 .002 .010 .034 .080 .138 .184 .193 .161 .107 .057 .024 .008 .002 .000 .000 .000 .000 .000 .000 .001 .005 .018 .047 .094 .148 .185 .185 .148 .094 .047 .018 .005 .001 .000 .000 .000 .000 .000 .000 .002 .008 .024 .057 .107 .161 .193 .184 .138 .080 .034 .010 .002 .000 .000 .000 .000 .000 .000 .001 .003 .009 .028 .064 .120 .178 .208 .187 .125 .058 .017 .002 .000 .000 .000 .000 .000 .000 .000 .000 .002 .008 .027 .068 .136 .209 .239 .191 .096 .023 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .004 .017 .060 .156 .280 .315 .167 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .008 .041 .158 .374 .418 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .012 .145 .843 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 .835 .152 .013 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .397 .376 .168 .047 .009 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .150 .300 .284 .168 .070 .022 .005 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .018 .081 .172 .230 .215 .151 .082 .035 .012 .003 .001 .000 .000 .000 .000 .000 .000 .000 .000 .002 .013 .046 .105 .168 .202 .187 .138 .081 .039 .015 .005 .001 .000 .000 .000 .000 .000 .000 .000 .001 .007 .025 .061 .115 .166 .189 .173 .128 .077 .037 .015 .004 .001 .000 .000 .000 .000 .000 .000 .001 .003 .012 .033 .071 .121 .167 .185 .167 .121 .071 .033 .012 .003 .001 .000 .000 .000 .000 .000 .000 .001 .004 .015 .037 .077 .128 .173 .189 .166 .115 .061 .025 .007 .001 .000 .000 .000 .000 .000 .000 .000 .001 .005 .015 .039 .081 .138 .187 .202 .168 .105 .046 .013 .002 .000 .000 .000 .000 .000 .000 .000 .000 .001 .003 .012 .035 .082 .151 .215 .230 .172 .081 .018 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .005 .022 .070 .168 .284 .300 .150 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .009 .047 .168 .376 .397 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .013 .152 .835 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 .826 .159 .014 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .377 .377 .179 .053 .011 .002 .000 .000 .000 .000 .000 .000 .000 .000 .000 .135 .285 .285 .180 .080 .027 .007 .001 .000 .000 .000 .000 .000 .000 .000 .014 .068 .154 .218 .218 .164 .095 .044 .017 .005 .001 .000 .000 .000 .000 .001 .009 .036 .087 .149 .192 .192 .153 .098 .051 .022 .008 .002 .001 .000 .000 .001 .005 .017 .047 .093 .145 .180 .180 .146 .098 .053 .024 .008 .002 .000 .000 .000 .002 .007 .022 .052 .096 .144 .176 .176 .144 .096 .052 .022 .000 .000 .000 .000 .001 .002 .008 .024 .053 .098 .146 .180 .180 .145 .093 .000 .000 .000 .000 .000 .000 .001 .002 .008 .022 .051 .098 .153 .192 .192 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .005 .017 .044 .095 .164 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .007 .027 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .002 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 3336-CDAppA.pdf 1/6/05 5:37 PM Page 5 Appendix A TABLE A.1 Tables Binomial probabilities [nCxpx(1 - p)n-x] (continued). P n x 15 16 17 18 19 0.01 .000 .000 .000 .000 .000 0.05 .000 .000 .000 .000 .000 0.10 .000 .000 .000 .000 .000 0.20 .000 .000 .000 .000 .000 0.30 .000 .000 .000 .000 .000 0.40 .001 .000 .000 .000 .000 0.50 .007 .002 .000 .000 .000 0.60 .047 .017 .005 .001 .000 0.70 .149 .087 .036 .009 .001 0.80 .218 .218 .154 .068 .014 0.90 .080 .180 .285 .285 .135 0.95 .011 .053 .179 .377 .377 0.99 .000 .001 .014 .159 .826 x 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 .818 .165 .016 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .358 .377 .189 .060 .013 .002 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .122 .270 .285 .190 .090 .032 .009 .002 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .012 .058 .137 .205 .218 .175 .109 .055 .022 .007 .002 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .007 .028 .072 .130 .179 .192 .164 .114 .065 .031 .012 .004 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .003 .012 .035 .075 .124 .166 .180 .160 .117 .071 .035 .015 .005 .001 .000 .000 .000 .000 .000 .000 .000 .000 .001 .005 .015 .037 .074 .120 .160 .176 .160 .120 .074 .037 .015 .005 .001 .000 .000 .000 .000 .000 .000 .000 .000 .001 .005 .015 .035 .071 .117 .160 .180 .166 .124 .075 .035 .012 .003 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .004 .012 .031 .065 .114 .164 .192 .179 .130 .072 .028 .007 .001 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .002 .007 .022 .055 .109 .175 .218 .205 .137 .058 .012 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .002 .009 .032 .090 .190 .285 .270 .122 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .002 .013 .060 .189 .377 .358 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .016 .165 .818 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 5 3336-CDAppA.pdf Appendix A 1/6/05 5:37 PM Page 6 Tables TABLE A.2 Cumulative Binomial Probabilities. P n x 0 1 2 0.01 0.980 1.000 1.000 0.05 0.903 0.998 1.000 0.10 0.810 0.990 1.000 0.20 0.640 0.960 1.000 0.30 0.490 0.910 1.000 0.40 0.360 0.840 1.000 0.50 0.250 0.750 1.000 0.60 0.160 0.640 1.000 0.70 0.090 0.510 1.000 0.80 0.040 0.360 1.000 0.90 0.010 0.190 1.000 0.95 0.003 0.098 1.000 0.99 0.000 0.020 1.000 x 0 1 2 3 0 1 2 0.970 1.000 1.000 1.000 0.857 0.993 1.000 1.000 0.729 0.972 0.999 1.000 0.512 0.896 0.992 1.000 0.343 0.784 0.973 1.000 0.216 0.648 0.936 1.000 0.125 0.500 0.875 1.000 0.064 0.352 0.784 1.000 0.027 0.216 0.657 1.000 0.008 0.104 0.488 1.000 0.001 0.028 0.271 1.000 0.000 0.007 0.143 1.000 0.000 0.000 0.030 1.000 0 1 2 3 4 0 1 2 3 4 0.961 0.999 1.000 1.000 1.000 0.815 0.986 1.000 1.000 1.000 0.656 0.948 0.996 1.000 1.000 0.410 0.819 0.973 0.998 1.000 0.240 0.652 0.916 0.992 1.000 0.130 0.475 0.821 0.974 1.000 0.063 0.313 0.688 0.938 1.000 0.026 0.179 0.525 0.870 1.000 0.008 0.084 0.348 0.760 1.000 0.002 0.027 0.181 0.590 1.000 0.000 0.004 0.052 0.344 1.000 0.000 0.000 0.014 0.185 1.000 0.000 0.000 0.001 0.039 1.000 0 1 2 3 4 5 0 1 2 3 4 5 0.951 0.999 1.000 1.000 1.000 1.000 0.774 0.977 0.999 1.000 1.000 1.000 0.590 0.919 0.991 1.000 1.000 1.000 0.328 0.737 0.942 0.993 1.000 1.000 0.168 0.528 0.837 0.969 0.998 1.000 0.078 0.337 0.683 0.913 0.990 1.000 0.031 0.187 0.500 0.812 0.969 1.000 0.010 0.087 0.317 0.663 0.922 1.000 0.002 0.031 0.163 0.472 0.832 1.000 0.000 0.007 0.058 0.263 0.672 1.000 0.000 0.000 0.009 0.081 0.410 1.000 0.000 0.000 0.001 0.023 0.226 1.000 0.000 0.000 0.000 0.001 0.049 1.000 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0.941 0.999 1.000 1.000 1.000 1.000 1.000 0.735 0.967 0.998 1.000 1.000 1.000 1.000 0.531 0.886 0.984 0.999 1.000 1.000 1.000 0.262 0.655 0.901 0.983 0.998 1.000 1.000 0.118 0.420 0.744 0.930 0.989 0.999 1.000 0.047 0.233 0.544 0.821 0.959 0.996 1.000 0.016 0.109 0.344 0.656 0.891 0.984 1.000 0.004 0.041 0.179 0.456 0.767 0.953 1.000 0.001 0.011 0.070 0.256 0.580 0.882 1.000 0.000 0.002 0.017 0.099 0.345 0.738 1.000 0.000 0.000 0.001 0.016 0.114 0.469 1.000 0.000 0.000 0.000 0.002 0.033 0.265 1.000 0.000 0.000 0.000 0.000 0.001 0.059 1.000 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0.932 0.998 1.000 1.000 1.000 1.000 1.000 1.000 0.698 0.956 0.996 1.000 1.000 1.000 1.000 1.000 0.478 0.850 0.974 0.997 1.000 1.000 1.000 1.000 0.210 0.577 0.852 0.967 0.995 1.000 1.000 1.000 0.082 0.329 0.647 0.874 0.971 0.996 1.000 1.000 0.028 0.159 0.420 0.710 0.904 0.981 0.998 1.000 0.008 0.063 0.227 0.500 0.773 0.938 0.992 1.000 0.002 0.019 0.096 0.290 0.580 0.841 0.972 1.000 0.000 0.004 0.029 0.126 0.353 0.671 0.918 1.000 0.000 0.000 0.005 0.033 0.148 0.423 0.790 1.000 0.000 0.000 0.000 0.003 0.026 0.150 0.522 1.000 0.000 0.000 0.000 0.000 0.004 0.044 0.302 1.000 0.000 0.000 0.000 0.000 0.000 0.002 0.068 1.000 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0.923 0.997 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.663 0.943 0.994 1.000 1.000 1.000 1.000 1.000 1.000 0.430 0.813 0.962 0.995 1.000 1.000 1.000 1.000 1.000 0.168 0.503 0.797 0.944 0.990 0.999 1.000 1.000 1.000 0.058 0.255 0.552 0.806 0.942 0.989 0.999 1.000 1.000 0.017 0.106 0.315 0.594 0.826 0.950 0.991 0.999 1.000 0.004 0.035 0.145 0.363 0.637 .0855 0.965 0.996 1.000 0.001 0.009 0.050 0.174 0.406 0.685 0.894 0.983 1.000 0.000 0.001 0.011 0.058 0.194 0.448 0.745 0.942 1.000 0.000 0.000 0.001 0.010 0.056 0.203 0.497 0.832 1.000 0.000 0.000 0.000 0.000 0.005 0.038 0.187 0.570 1.000 0.000 0.000 0.000 0.000 0.000 0.006 0.057 0.337 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.003 0.077 1.000 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0.914 0.997 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.630 0.929 0.992 0.999 1.000 1.000 1.000 1.000 1.000 1.000 0.387 0.775 0.947 0.992 0.999 1.000 1.000 1.000 1.000 1.000 0.134 0.436 0.738 0.914 0.980 0.997 1.000 1.000 1.000 1.000 0.040 0.196 0.463 0.730 0.901 0.975 0.996 1.000 1.000 1.000 0.010 0.071 0.232 0.483 0.733 0.901 0.975 0.996 1.000 1.000 0.002 0.020 0.090 0.254 0.500 0.746 0.910 0.980 0.998 1.000 0.000 0.004 0.025 0.099 0.267 0.517 0.768 0.929 0.990 1.000 0.000 0.000 0.004 0.025 0.099 0.270 0.537 0.804 0.960 1.000 0.000 0.000 0.000 0.003 0.020 0.086 0.262 0.564 0.866 1.000 0.000 0.000 0.000 0.000 0.001 0.008 0.053 0.225 0.613 1.000 0.000 0.000 0.000 0.000 0.000 0.001 0.008 0.071 0.370 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.003 0.086 1.000 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0.904 0.996 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.599 0.914 0.988 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.349 0.736 0.930 0.987 0.998 1.000 1.000 1.000 1.000 1.000 1.000 0.107 0.376 0.678 0.879 0.967 0.994 0.999 1.000 1.000 1.000 1.000 0.028 0.149 0.383 0.650 0.850 0.953 0.989 0.998 1.000 1.000 1.000 0.006 0.046 0.167 0.382 0.633 0.834 0.945 0.988 0.998 1.000 1.000 0.001 0.011 0.055 0.172 0.377 0.623 0.828 0.945 0.989 0.999 1.000 0.000 0.002 0.012 0.055 0.166 0.367 0.618 0.833 0.954 0.994 1.000 0.000 0.000 0.002 0.011 0.047 0.150 0.350 0.617 0.851 0.972 1.000 0.000 0.000 0.000 0.001 0.006 0.033 0.121 0.322 0.624 0.893 1.000 0.000 0.000 0.000 0.000 0.000 0.002 0.013 0.070 0.264 0.651 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.012 0.086 0.401 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.004 0.096 1.000 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 0.895 0.995 1.000 0.569 0.898 0.985 0.314 0.697 0.910 0.086 0.322 0.617 0.020 0.113 0.313 0.004 0.030 0.119 0.000 0.006 0.033 0.000 0.001 0.006 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 1 2 2 6 3336-CDAppA.pdf 1/6/05 5:37 PM Page 7 Appendix A TABLE A.2 Tables Cumulative Binomial Probabilities (continued). P n x 3 4 5 6 7 8 9 10 11 0.01 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.05 0.998 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.10 0.981 0.997 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.20 0.839 0.950 0.988 0.998 1.000 1.000 1.000 1.000 1.000 0.30 0.570 0.790 0.922 0.978 0.996 0.999 1.000 1.000 1.000 0.40 0.296 0.533 0.753 0.901 0.971 0.994 0.999 1.000 1.000 0.50 0.113 0.274 0.500 0.726 0.887 0.967 0.994 1.000 1.000 0.60 0.029 0.099 0.247 0.467 0.704 0.881 0.970 0.996 1.000 0.70 0.004 0.022 0.078 0.210 0.430 0.687 0.887 0.980 1.000 0.80 0.000 0.002 0.012 0.050 0.161 0.383 0.678 0.914 1.000 0.90 0.000 0.000 0.000 0.003 0.019 0.090 0.303 0.686 1.000 0.95 0.000 0.000 0.000 0.000 0.002 0.015 0.102 0.431 1.000 0.99 0.000 0.000 0.000 0.000 0.000 0.000 0.005 0.105 1.000 x 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12 0.886 0.994 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.540 0.882 0.980 0.998 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.282 0.659 0.889 0.974 0.996 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.069 0.275 0.558 0.795 0.927 0.981 0.996 0.999 1.000 1.000 1.000 1.000 1.000 0.014 0.085 0.253 0.493 0.724 0.882 0.961 0.991 0.998 1.000 1.000 1.000 1.000 0.002 0.020 0.083 0.225 0.438 0.665 0.842 0.943 0.985 0.997 1.000 1.000 1.000 0.000 0.003 0.019 0.073 0.194 0.387 0.613 0.806 0.927 0.981 0.997 1.000 1.000 0.000 0.000 0.003 0.015 0.057 0.158 0.335 0.562 0.775 0.917 0.980 0.998 1.000 0.000 0.000 0.000 0.002 0.009 0.039 0.118 0.276 0.507 0.747 0.915 0.986 1.000 0.000 0.000 0.000 0.000 0.001 0.004 0.019 0.073 0.205 0.442 0.725 0.931 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.004 0.026 0.111 0.341 0.718 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.020 0.118 0.460 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.006 0.114 1.000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0.878 0.993 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.513 0.865 0.975 0.997 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.254 0.621 0.866 0.966 0.994 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.055 0.234 0.502 0.747 0.901 0.970 0.993 0.999 1.000 1.000 1.000 1.000 1.000 1.000 0.010 0.064 0.202 0.421 0.654 0.835 0.938 0.982 0.996 0.999 1.000 1.000 1.000 1.000 0.001 0.013 0.058 0.169 0.353 0.574 0.771 0.902 0.968 0.992 0.999 1.000 1.000 1.000 0.000 0.002 0.011 0.046 0.133 0.291 0.500 0.709 0.867 0.954 0.989 0.998 1.000 1.000 0.000 0.000 0.001 0.008 0.032 0.098 0.229 0.426 0.647 0.831 0.942 0.987 0.999 1.000 0.000 0.000 0.000 0.001 0.004 0.018 0.062 0.165 0.346 0.579 0.798 0.936 0.990 1.000 0.000 0.000 0.000 0.000 0.000 0.001 0.007 0.030 0.099 0.253 0.498 0.766 0.945 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.006 0.034 0.134 0.379 0.746 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.003 0.025 0.135 0.487 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.007 0.122 1.000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.869 0.992 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.488 0.847 0.970 0.996 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.229 0.585 0.842 0.956 0.991 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.044 0.198 0.448 0.698 0.870 0.956 0.988 0.998 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.007 0.047 0.161 0.355 0.584 0.781 0.907 0.969 0.992 0.998 1.000 1.000 1.000 1.000 1.000 0.001 0.008 0.040 0.124 0.279 0.486 0.692 0.850 0.942 0.982 0.996 0.999 1.000 1.000 1.000 0.000 0.001 0.006 0.029 0.090 0.212 0.395 0.605 0.788 0.910 0.971 0.994 0.999 1.000 1.000 0.000 0.000 0.001 0.004 0.018 0.058 0.150 0.308 0.514 0.721 0.876 0.960 0.992 0.999 1.000 0.000 0.000 0.000 0.000 0.002 0.008 0.031 0.093 0.219 0.416 0.645 0.839 0.953 0.993 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.012 0.044 0.130 0.302 0.552 0.802 0.956 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.009 0.044 0.158 0.415 0.771 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.004 0.030 0.153 0.512 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.008 0.131 1.000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.860 0.990 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.463 0.829 0.964 0.995 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.206 0.549 0.816 0.944 0.987 0.998 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.035 0.167 0.398 0.648 0.836 0.939 0.982 0.996 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.005 0.035 0.127 0.297 0.515 0.722 0.869 0.950 0.985 0.996 0.999 1.000 1.000 1.000 1.000 1.000 0.000 0.005 0.027 0.091 0.217 0.403 0.610 0.787 0.905 0.966 0.991 0.998 1.000 1.000 1.000 1.000 0.000 0.000 0.004 0.018 0.059 0.151 0.304 0.500 0.696 0.849 0.941 0.982 0.996 1.000 1.000 1.000 0.000 0.000 0.000 0.002 0.009 0.034 0.095 0.213 0.390 0.597 0.783 0.909 0.973 0.995 1.000 1.000 0.000 0.000 0.000 0.000 0.001 0.004 0.015 0.050 0.131 0.278 0.485 0.703 0.873 0.965 0.995 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.004 0.018 0.061 0.164 0.352 0.602 0.833 0.965 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.013 0.056 0.184 0.451 0.794 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.005 0.036 0.171 0.537 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.010 0.140 1.000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 7 3336-CDAppA.pdf Appendix A 1/6/05 5:37 PM Page 8 Tables TABLE A.2 Cumulative Binomial Probabilities (continued). P 8 n 16 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.01 0.851 0.989 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.05 0.440 0.811 0.957 0.993 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.10 0.185 0.515 0.789 0.932 0.983 0.997 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.20 0.028 0.141 0.352 0.598 0.798 0.918 0.973 0.993 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.30 0.003 0.026 0.099 0.246 0.450 0.660 0.825 0.926 0.974 0.993 0.998 1.000 1.000 1.000 1.000 1.000 1.000 0.40 0.000 0.003 0.018 0.065 0.167 0.329 0.527 0.716 0.858 0.942 0.981 0.995 0.999 1.000 1.000 1.000 1.000 0.50 0.000 0.000 0.002 0.011 0.038 0.105 0.227 0.402 0.598 0.773 0.895 0.962 0.989 0.998 1.000 1.000 1.000 0.60 0.000 0.000 0.000 0.001 0.005 0.019 0.058 0.142 0.284 0.473 0.671 0.833 0.935 0.982 0.997 1.000 1.000 0.70 0.000 0.000 0.000 0.000 0.000 0.002 0.007 0.026 0.074 0.175 0.340 0.550 0.754 0.901 0.974 0.997 1.000 0.80 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.007 0.027 0.082 0.202 0.402 0.648 0.859 0.972 1.000 0.90 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.003 0.017 0.068 0.211 0.485 0.815 1.000 0.95 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.007 0.043 0.189 0.560 1.000 0.99 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.011 0.149 1.000 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.843 0.988 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.418 0.792 0.950 0.991 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.167 0.482 0.762 0.917 0.978 0.995 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.023 0.118 0.310 0.549 0.758 0.894 0.962 0.989 0.997 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.002 0.019 0.077 0.202 0.389 0.597 0.775 0.895 0.960 0.987 0.997 0.999 1.000 1.000 1.000 1.000 1.000 1.000 0.000 0.002 0.012 0.046 0.126 0.264 0.448 0.641 0.801 0.908 0.965 0.989 0.997 1.000 1.000 1.000 1.000 1.000 0.000 0.000 0.001 0.006 0.025 0.072 0.166 0.315 0.500 0.685 0.834 0.928 0.975 0.994 0.999 1.000 1.000 1.000 0.000 0.000 0.000 0.000 0.003 0.011 0.035 0.092 0.199 0.359 0.552 0.736 0.874 0.954 0.988 0.998 1.000 1.000 0.000 0.000 0.000 0.000 0.000 0.001 0.003 0.013 0.040 0.105 0.225 0.403 0.611 0.798 0.923 0.981 0.998 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.003 0.011 0.038 0.106 0.242 0.451 0.690 0.882 0.977 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.005 0.022 0.083 0.238 0.518 0.833 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.009 0.050 0.208 0.582 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.012 0.157 1.000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0.835 0.986 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.397 0.774 0.942 0.989 0.998 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.150 0.450 0.734 0.902 0.972 0.994 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.018 0.099 0.271 0.501 0.716 0.867 0.949 0.984 0.996 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.002 0.014 0.060 0.165 0.333 0.534 0.722 0.859 0.940 0.979 0.994 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.000 0.001 0.008 0.033 0.094 0.209 0.374 0.563 0.737 0.865 0.942 0.980 0.994 0.999 1.000 1.000 1.000 1.000 1.000 0.000 0.000 0.001 0.004 0.015 0.048 0.119 0.240 0.407 0.593 0.760 0.881 0.952 0.985 0.996 0.999 1.000 1.000 1.000 0.000 0.000 0.000 0.000 0.001 0.006 0.020 0.058 0.135 0.263 0.437 0.626 0.791 0.906 0.967 0.992 0.999 1.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.006 0.021 0.060 0.141 0.278 0.466 0.667 0.835 0.940 0.986 0.998 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.004 0.016 0.051 0.133 0.284 0.499 0.729 0.901 0.982 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.006 0.028 0.098 0.266 0.550 0.850 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.011 0.058 0.226 0.603 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.014 0.165 1.000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.826 0.985 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.377 0.755 0.933 0.987 0.998 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.135 0.420 0.705 0.885 0.965 0.991 0.998 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.014 0.083 0.237 0.455 0.673 0.837 0.932 0.977 0.993 0.998 1.000 1.000 1.000 1.000 1.000 0.001 0.010 0.046 0.133 0.282 0.474 0.666 0.818 0.916 0.967 0.989 0.997 0.999 1.000 1.000 0.000 0.001 0.005 0.023 0.070 0.163 0.308 0.488 0.667 0.814 0.912 0.965 0.988 0.997 0.999 0.000 0.000 0.000 0.002 0.010 0.032 0.084 0.180 0.324 0.500 0.676 0.820 0.916 0.968 0.990 0.000 0.000 0.000 0.000 0.001 0.003 0.012 0.035 0.088 0.186 0.333 0.512 0.692 0.837 0.930 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.003 0.011 0.033 0.084 0.182 0.334 0.526 0.718 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.007 0.023 0.068 0.163 0.327 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.009 0.035 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 3336-CDAppA.pdf 1/6/05 5:37 PM Page 9 Appendix A TABLE A.2 Tables Cumulative Binomial Probabilities (continued). P n x 15 16 17 18 19 0.01 1.000 1.000 1.000 1.000 1.000 0.05 1.000 1.000 1.000 1.000 1.000 0.10 1.000 1.000 1.000 1.000 1.000 0.20 1.000 1.000 1.000 1.000 1.000 0.30 1.000 1.000 1.000 1.000 1.000 0.40 1.000 1.000 1.000 1.000 1.000 0.50 0.998 1.000 1.000 1.000 1.000 0.60 0.977 0.995 0.999 1.000 1.000 0.70 0.867 0.954 0.990 0.999 1.000 0.80 0.545 0.763 0.917 0.986 1.000 0.90 0.115 0.295 0.580 0.865 1.000 0.95 0.013 0.067 0.245 0.623 1.000 0.99 0.000 0.001 0.015 0.174 1.000 x 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0.818 0.983 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.358 0.736 0.925 0.984 0.997 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.122 0.392 0.677 0.867 0.957 0.989 0.998 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.012 0.069 0.206 0.411 0.630 0.804 0.913 0.968 0.990 0.997 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.001 0.008 0.035 0.107 0.238 0.416 0.608 0.772 0.887 0.952 0.983 0.995 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.000 0.001 0.004 0.016 0.051 0.126 0.250 0.416 0.596 0.755 0.872 0.943 0.979 0.994 0.998 1.000 1.000 1.000 1.000 1.000 1.000 0.000 0.000 0.000 0.001 0.006 0.021 0.058 0.132 0.252 0.412 0.588 0.748 0.868 0.942 0.979 0.994 0.999 1.000 1.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000 0.002 0.006 0.021 0.057 0.128 0.245 0.404 0.584 0.750 0.874 0.949 0.984 0.996 0.999 1.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.005 0.017 0.048 0.113 0.228 0.392 0.584 0.762 0.893 0.965 0.992 0.999 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.003 0.010 0.032 0.087 0.196 0.370 0.589 0.794 0.931 0.988 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.011 0.043 0.133 0.323 0.608 0.878 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.003 0.016 0.075 0.264 0.642 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.017 0.182 1.000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 9 3336-CDAppA.pdf Appendix A 1/6/05 5:37 PM Page 10 Tables TABLE A.3 10 e x Poisson Probabilities . x! x 0 1 2 3 0.005 0.9950 0.0050 0.0000 0.0000 0.01 0.9900 0.0099 0.0000 0.0000 0.02 0.9802 0.0196 0.0002 0.0000 0.03 0.9704 0.0291 0.0004 0.0000 l 0.04 0.9608 0.0384 0.0008 0.0000 0.05 0.9512 0.0476 0.0012 0.0000 0.06 0.9418 0.0565 0.0017 0.0000 0.07 0.9324 0.0653 0.0023 0.0001 0.08 0.9231 0.0738 0.0030 0.0001 0.09 0.9139 0.0823 0.0037 0.0001 x 0 1 2 3 4 5 6 7 0.1 0.9048 0.0905 0.0045 0.0002 0.0000 0.0000 0.0000 0.0000 0.2 0.8187 0.1637 0.0164 0.0011 0.0001 0.0000 0.0000 0.0000 0.3 0.7408 0.2222 0.0333 0.0033 0.0003 0.0000 0.0000 0.0000 0.4 0.6703 0.2681 0.0536 0.0072 0.0007 0.0001 0.0000 0.0000 0.5 0.6065 0.3033 0.0758 0.0126 0.0016 0.0002 0.0000 0.0000 0.6 0.5488 0.3293 0.0988 0.0198 0.0030 0.0004 0.0000 0.0000 0.7 0.4966 0.3476 0.1217 0.0284 0.0050 0.0007 0.0001 0.0000 0.8 0.4493 0.3595 0.1438 0.0383 0.0077 0.0012 0.0002 0.0000 0.9 0.4066 0.3659 0.1647 0.0494 0.0111 0.0020 0.0003 0.0000 1.0 0.3679 0.3679 0.1839 0.0613 0.0153 0.0031 0.0005 0.0001 x 0 1 2 3 4 5 6 7 8 9 1.1 0.3329 0.3662 0.2014 0.0738 0.0203 0.0045 0.0008 0.0001 0.0000 0.0000 1.2 0.3012 0.3614 0.2169 0.0867 0.0260 0.0062 0.0012 0.0002 0.0000 0.0000 1.3 0.2725 0.3543 0.2303 0.0998 0.0324 0.0084 0.0018 0.0003 0.0001 0.0000 1.4 0.2466 0.3452 0.2417 0.1128 0.0395 0.0111 0.0026 0.0005 0.0001 0.0000 1.5 0.2231 0.3347 0.2510 0.1255 0.0471 0.0141 0.0035 0.0008 0.0001 0.0000 1.6 0.2019 0.3230 0.2584 0.1378 0.0551 0.0176 0.0047 0.0011 0.0002 0.0000 1.7 0.1827 0.3106 0.2640 0.1496 0.0636 0.0216 0.0061 0.0015 0.0003 0.0001 1.8 0.1653 0.2975 0.2678 0.1607 0.0723 0.0260 0.0078 0.0020 0.0005 0.0001 1.9 0.1496 0.2842 0.2700 0.1710 0.0812 0.0309 0.0098 0.0027 0.0006 0.0001 2.0 0.1353 0.2707 0.2707 0.1804 0.0902 0.0361 0.0120 0.0034 0.0009 0.0002 x 0 1 2 3 4 5 6 7 8 9 10 11 12 2.1 0.1225 0.2572 0.2700 0.1890 0.0992 0.0417 0.0146 0.0044 0.0011 0.0003 0.0001 0.0000 0.0000 2.2 0.1108 0.2438 0.2681 0.1966 0.1082 0.0476 0.0174 0.0055 0.0015 0.0004 0.0001 0.0000 0.0000 2.3 0.1003 0.2306 0.2652 0.2033 0.1169 0.0538 0.0206 0.0068 0.0019 0.0005 0.0001 0.0000 0.0000 2.4 0.0907 0.2177 0.2613 0.2090 0.1254 0.0602 0.0241 0.0083 0.0025 0.0007 0.0002 0.0000 0.0000 2.5 0.0821 0.2052 0.2565 0.2138 0.1336 0.0668 0.0278 0.0099 0.0031 0.0009 0.0002 0.0000 0.0000 2.6 0.0743 0.1931 0.2510 0.2176 0.1414 0.0735 0.0319 0.0118 0.0038 0.0011 0.0003 0.0001 0.0000 2.7 0.0672 0.1815 0.2450 0.2205 0.1488 0.0804 0.0362 0.0139 0.0047 0.0014 0.0004 0.0001 0.0000 2.8 0.0608 0.1703 0.2384 0.2225 0.1557 0.0872 0.0407 0.0163 0.0057 0.0018 0.0005 0.0001 0.0000 2.9 0.0550 0.1596 0.2314 0.2237 0.1622 0.0940 0.0455 0.0188 0.0068 0.0022 0.0006 0.0002 0.0000 3.0 0.0498 0.1494 0.2240 0.2240 0.1680 0.1008 0.0504 0.0216 0.0081 0.0027 0.0008 0.0002 0.0001 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 3.1 0.0450 0.1397 0.2165 0.2237 0.1733 0.1075 0.0555 0.0246 0.0095 0.0033 0.0010 0.0003 0.0001 0.0000 0.0000 3.2 0.0408 0.1304 0.2087 0.2226 0.1781 0.1140 0.0608 0.0278 0.0111 0.0040 0.0013 0.0004 0.0001 0.0000 0.0000 3.3 0.0369 0.1217 0.2008 0.2209 0.1823 0.1203 0.0662 0.0312 0.0129 0.0047 0.0016 0.0005 0.0001 0.0000 0.0000 3.4 0.0334 0.1135 0.1929 0.2186 0.1858 0.1264 0.0716 0.0348 0.0148 0.0056 0.0019 0.0006 0.0002 0.0000 0.0000 3.5 0.0302 0.1057 0.1850 0.2158 0.1888 0.1322 0.0771 0.0385 0.0169 0.0066 0.0023 0.0007 0.0002 0.0001 0.0000 3.6 0.0273 0.0984 0.1771 0.2125 0.1912 0.1377 0.0826 0.0425 0.0191 0.0076 0.0028 0.0009 0.0003 0.0001 0.0000 3.7 0.0247 0.0915 0.1692 0.2087 0.1931 0.1429 0.0881 0.0466 0.0215 0.0089 0.0033 0.0011 0.0003 0.0001 0.0000 3.8 0.0224 0.0850 0.1615 0.2046 0.1944 0.1477 0.0936 0.0508 0.0241 0.0102 0.0039 0.0013 0.004 0.0001 0.0000 3.9 0.0202 0.0789 0.1539 0.2001 0.1951 0.1522 0.0989 0.0551 0.0269 0.0116 0.0045 0.0016 0.0005 0.0002 0.0000 4.0 0.0183 0.0733 0.1465 0.1954 0.1954 0.1563 0.1042 0.0595 0.0298 0.0132 0.0053 0.0019 0.0006 0.0002 0.0001 x 0 1 2 3 4 5 6 7 8 9 10 11 4.1 0.0166 0.0679 0.1393 0.1904 0.1951 0.1600 0.1093 0.0640 0.0328 0.0150 0.0061 0.0023 4.2 0.0150 0.0630 0.1323 0.1852 0.1944 0.1633 0.1143 0.0686 0.0360 0.0168 0.0071 0.0027 4.3 0.0136 0.0583 0.1254 0.1798 0.1933 0.1662 0.1191 0.0732 0.0393 0.0188 0.0081 0.0032 4.4 0.0123 0.0540 0.1188 0.1743 0.1917 0.1687 0.1237 0.0778 0.0428 0.0209 0.0092 0.0037 4.5 0.0111 0.0500 0.1125 0.1687 0.1898 0.1708 0.1281 0.0824 0.0463 0.0232 0.0104 0.0043 4.6 0.0101 0.0462 0.1063 0.1631 0.1875 0.1725 0.1323 0.0869 0.0500 0.0255 0.0118 0.0049 4.7 0.0091 0.0427 0.1005 0.1574 0.1849 0.1738 0.1362 0.0914 0.0537 0.0281 0.0132 0.0056 4.8 0.0082 0.0395 0.0948 0.1517 0.1820 0.1747 0.1398 0.0959 0.0575 0.0307 0.0147 0.0064 4.9 0.0074 0.0365 0.0894 0.1460 0.1789 0.1753 0.1432 0.1002 0.0614 0.0334 0.0164 0.0073 5.0 0.0067 0.0337 0.0842 0.1404 0.1755 0.1755 0.1462 0.1044 0.0653 0.0363 0.0181 0.0082 3336-CDAppA.pdf 1/6/05 5:37 PM Page 11 Appendix A TABLE A.3 Tables e x Poisson Probabilities (continued). x! l x 12 13 14 15 4.1 0.0008 0.0002 0.0001 0.0000 4.2 0.0009 0.0003 0.0001 0.0000 4.3 0.0011 0.0004 0.0001 0.0000 4.4 0.0013 0.0005 0.0001 0.0000 4.5 0.0016 0.0006 0.0002 0.0001 4.6 0.0019 0.0007 0.0002 0.0001 4.7 0.0022 0.0008 0.0003 0.0001 4.8 0.0026 0.0009 0.0003 0.0001 4.9 0.0030 0.0011 0.0004 0.0001 5.0 0.0034 0.0013 0.0005 0.0002