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statistics alive

Questions and Answers of Statistics Alive

10. Tax Audits In Exercise 9, we suggested that the IRS assigns auditing rates per state by randomly selecting 50 auditing percentages from a normal distribution with a mean equal to 1.55% and a
11. Your Favorite Sport Among the 10 most popular sports, men include competition-type sports—pool and billiards, basketball, and softball—whereas women include aerobics, running, hiking, and
12. Normal Temperatures In Exercise 15 (Chapter 1 Review), Allen Shoemaker derived a distribution of human body temperatures, which has a distinct mound-shape.14 Suppose we assume that the
13. Test Scores The scores on a national achievement test were approximately normally distributed, with a mean of 540 and a standard deviation of 110.a. If you achieved a score of 680, how far, in
30. Use Table 1 in Appendix I to find the following: a. P(x 4) for n=10, p = .4 d. P(x6) for n=15, p=.6 e. P(3
Answer the question for a normal random variable x with mean m and standard deviation s specified in the exercises. 41. u 1.2 andor =.15. Find P(1.35 < x < 1.50).
Cerebral blood flow (CBF) in the brains of healthy people is normally distributed with a mean of 74 and a standard deviation of 16. Use this information to answer 53. What proportion of healthy
Cerebral blood flow (CBF) in the brains of healthy people is normally distributed with a mean of 74 and a standard deviation of 16. Use this information to answer 54. What proportion of healthy
Cerebral blood flow (CBF) in the brains of healthy people is normally distributed with a mean of 74 and a standard deviation of 16. Use this information to answer 55. If a person has a CBF reading
56. Washers The life span of a type of automatic washer is approximately normally distributed with mean and standard deviation equal to 10.5 and 3.0 years, respectively. If this type of washer is
57. How Long Is the Test? The average length of time required to complete a college achievement test is approximately normal with a mean of 70 minutes and a standard deviation of 12 minutes. When
58. Filling Soda Cups A soft drink machine can be regulated to discharge an average of m ounces per cup. If the ounces of fill are normally distributed, with standard deviation equal to .3 ounce,
59. Gestation Times The Biology Data Book reports that the gestation time for human babies averages 278 days with a standard deviation of 12 days.3 Suppose that these gestation times are normally
60. Introvert or Extrovert? A psychological introvert–extrovert test produced scores that had a normal distribution with mean and standard deviation 75 and 12, respectively. If we wish to designate
61. Hamburger Meat A supermarket prepares its“1-pound” packages of ground beef so that there will be a variety of weights, some slightly more and some slightly less than 1 pound. Suppose that the
Assume that the heights of American men are normally distributed with a mean of 176.5 centimeters and a standard deviation of 8.9 centimeters. Use this information to answer 52. Of the 44 presidents
Assume that the heights of American men are normally distributed with a mean of 176.5 centimeters and a standard deviation of 8.9 centimeters. Use this information to answer 51. President Donald
Answer the question for a normal random variable x with mean m and standard deviation s specified in the exercises. 42.35 and =10. Find a value of x that has area .01 to its right.
Answer the question for a normal random variable x with mean m and standard deviation s specified in the exercises. 43. = 50 and or=15. Would it be unusual to observe the value x =0? Explain.
Answer the question for a normal random variable x with mean m and standard deviation s specified in the exercises. 44. Unknown mean and =2. If P(x > 7.5)=.8023, find .
Answer the question for a normal random variable x with mean m and standard deviation s specified in the exercises. 45. Unknown mean and standard deviation . If P(x4)= .9772 and P(x >5)=.9332,
The weights of 3-month-old babies are normally distributed—baby boys with a mean of 6.4 kilograms and a standard deviation of 0.7, and baby girls with a mean of 5.9 kilograms and a standard
The weights of 3-month-old babies are normally distributed—baby boys with a mean of 6.4 kilograms and a standard deviation of 0.7, and baby girls with a mean of 5.9 kilograms and a standard
The weights of 3-month-old babies are normally distributed—baby boys with a mean of 6.4 kilograms and a standard deviation of 0.7, and baby girls with a mean of 5.9 kilograms and a standard
Assume that the heights of American men are normally distributed with a mean of 176.5 centimeters and a standard deviation of 8.9 centimeters. Use this information to answer 49. What proportion of
Assume that the heights of American men are normally distributed with a mean of 176.5 centimeters and a standard deviation of 8.9 centimeters. Use this information to answer 50. What is the
62. Christmas Trees The diameters of Douglas firs grown at a Christmas tree farm are normally distributed with a mean of 10 centimeters and a standard deviation of 3.75 centimeters.a. What proportion
63. Braking Distances For a car traveling 65 kilometers per hour (km/h), the distance required to brake to a stop is normally distributed with a mean of 43 meters4 and a standard deviation of 5
64. A Phosphate Mine The discharge of suspended solids from a phosphate mine is normally distributed, with a mean daily discharge of 27 milligrams per liter(mg/l) and a standard deviation of 14 mg/l.
Can the normal approximation be used to approximate probabilities for the binomial random variable x, with values for n and p given? If not, is there another approximation that you could use? 3. n
Can the normal approximation be used to approximate probabilities for the binomial random variable x, with values for n and p given? If not, is there another approximation that you could use? 4. n
Find the mean and standard deviation for the binomial random variable x using the information. Then use the correction for continuity and approximate the probabilities using the normal approximation.
Find the mean and standard deviation for the binomial random variable x using the information. Then use the correction for continuity and approximate the probabilities using the normal
Find the mean and standard deviation for the binomial random variable x using the information. Then use the correction for continuity and approximate the probabilities using the normal
Find the mean and standard deviation for the binomial random variable x using the information. Then use the correction for continuity and approximate the probabilities using the normal
Find the mean and standard deviation for the binomial random variable x using the information. Then use the correction for continuity and approximate the probabilities using the normal
Find the mean and standard deviation for the binomial random variable x using the information. Then use the correction for continuity and approximate the probabilities using the normal
Find the mean and standard deviation for the binomial random variable x using the information. Then use the correction for continuity and approximate the probabilities using the normal approximation.
Can the normal approximation be used to approximate probabilities for the binomial random variable x, with values for n and p given? If not, is there another approximation that you could use? 2. n
Can the normal approximation be used to approximate probabilities for the binomial random variable x, with values for n and p given? If not, is there another approximation that you could use? 1. n 25
65. Sunflowers An article in the Annals of Botany investigated whether the stem diameters of the dicot sunflower would change depending on whether the plant was left to sway freely in the wind or was
66. Economic Forecasts One method of arriving at economic forecasts is to use a consensus approach. A forecast is obtained from each of a large number of analysts, and the average of these individual
67. Bacteria in Drinking Water Suppose the numbers of a particular type of bacteria in samples of 1 milliliter(ml) of drinking water tend to be approximately normally distributed, with a mean of 85
68. Mall Rats An article in American Demographics claims that more than twice as many shoppers are out shopping on the weekends than during the week.7 Not only that, such shoppers also spend more
69. Pulse Rates What’s a normal pulse rate? That depends on a variety of factors. Pulse rates between 60 and 100 beats per minute are considered normal for children over 10 and adults.8 Suppose
70. Bearing Diameters A machine operation produces bearings whose diameters are normally distributed, with mean and standard deviation equal to .498 and .002, respectively. If specifications require
Use the normal curve to approximate the probability that x58, 9, or 10 for a binomial random variable with n525 and p5.5. Compare this approximation to the exact binomial probability.
The reliability of an electrical fuse is the probability that a fuse, chosen at random from production, will function under its designed conditions. A random sample of 1000 fuses was tested and x527
A soda manufacturer was fairly certain that her brand had a 10% share of the market. In a survey involving 2500 soda drinkers, x5211 preferred her brand. If the 10% figure is correct, find the
Using Table 1 in Appendix I, find the exact values for the binomial probabilities. Then approximate the probabilities using the normal approximation with the correction for continuity. Compare your
15. Locate the interval m62s on the x-axis of the histogram.What is the probability that x will fall into this interval?Use the probability distribution for the random variable x to answer X 0 1 2 3
Draw five cards randomly from a standard deck of 52 cards, and let x be the number of red cards in the draw. Evaluate the probabilities 24. P(x=0)
Let x be the number of successes observed in a sample of n=5 items selected from a population of N =10. Suppose that of the N =10 items, M =6 are considered “successes.” Find the probabilities
Let x be the number of successes observed in a sample of n=5 items selected from a population of N =10. Suppose that of the N =10 items, M =6 are considered “successes.” Find the probabilities
Let x be the number of successes observed in a sample of n=4 items selected from a population of N =8. Suppose that of the N =8 items, M =5 are considered “successes.” Find the probabilities 10.
Let x be the number of successes observed in a sample of n=4 items selected from a population of N =8. Suppose that of the N =8 items, M =5 are considered “successes.” Find the probabilities 9.
Let x be the number of successes observed in a sample of n=4 items selected from a population of N =8. Suppose that of the N =8 items, M =5 are considered “successes.” Find the probabilities 8.
Find the probabilities 7. CC C 4
Find the probabilities 6. CC 2 7 C 3 3
Find the probabilities 5. 2 CC C
Find the probabilities 4. CC C 4 3 2
Let x be the number of successes observed in a sample of n=5 items selected from a population of N =10. Suppose that of the N =10 items, M =6 are considered “successes.” Find the probabilities
Let x be a hypergeometric random variable with N =15, n=3, and M =4. 14. Calculate p(0), p(1), p(2), and p(3).
Draw five cards randomly from a standard deck of 52 cards, and let x be the number of red cards in the draw. Evaluate the probabilities 23. P(x=3)
Draw five cards randomly from a standard deck of 52 cards, and let x be the number of red cards in the draw. Evaluate the probabilities 22. P(x=5)
A candy dish contains five brown and three red M&Ms. A child selects three M&Ms without checking the colors. 21. Write down p(x), the probability distribution for x, the number of red M&Ms in the
A candy dish contains five brown and three red M&Ms. A child selects three M&Ms without checking the colors. 20. What is the probability that all the M&Ms are brown?
A candy dish contains five brown and three red M&Ms. A child selects three M&Ms without checking the colors. 19. What is the probability that the M&Ms are all red?
A candy dish contains five brown and three red M&Ms. A child selects three M&Ms without checking the colors. 18. What is the probability that there are two brown and one red M&Ms in the selection?
Let x be a hypergeometric random variable with N =15, n=3, and M =4. 17. What portion of the population of measurements fall into the interval (m 62s )? Into the interval (m 63s )?Do the results
Let x be a hypergeometric random variable with N =15, n=3, and M =4. 16. Use the formulas given in this section to calculate = E(x) and .
Let x be a hypergeometric random variable with N =15, n=3, and M =4. 15. Construct a probability histogram for x.
Find the probabilities 3. CAC C 2 2
Find the probabilities 2. CC 3
1. Under what conditions would you use the hypergeometric probability distribution to calculate the probability of x successes in n trials?
14. Website Traffic The number of visits to a website is known to have a Poisson distribution with a mean of 8 visits per minute.a. What is the probability distribution for x, the number of visits
13. Consumer Complaints The number of calls to a consumer hotline has a Poisson distribution with an average of 5 calls every 30 minutes.a. What is the probability that there are more than 8 calls
12. Bankrupt? The number of bankruptcies filed in the district court has a Poisson distribution with an average of 5 per week.a. What is the probability that there will be no bankruptcy filings
Let x be a binomial random variable, calculate the exact binomial probability using Table 1 in Appendix I. Then calculate the probability using the Poisson approximation.Compare your results. Is the
Let x be a binomial random variable, calculate the exact binomial probability using Table 1 in Appendix I. Then calculate the probability using the Poisson approximation.Compare your results. Is the
Let x be a binomial random variable, calculate the exact binomial probability using Table 1 in Appendix I. Then calculate the probability using the Poisson approximation.Compare your results. Is the
Let x be a Poisson random variable, find the probabilities for x using Table 2 in Appendix I. 8. u 2.5; P(x5), P(x
Let x be a Poisson random variable, find the probabilities for x using Table 2 in Appendix I. 7. =0.8; P(x=0), P(x2), P(x>2), and P(2x4).
Let x be a Poisson random variable, find the probabilities for x using Table 2 in Appendix I. 6. =3; P(x3), P(x>3), P(x=3), and P(3x5).
15. Be Careful at Work! Work-related accidents at a construction site tend to have a Poisson distribution with an average of 2 accidents per week.a. What is the probability that there will be no
16. Babies! The number of births at the local hospital has a Poisson distribution with an average of 6 per day.a. What is the probability distribution for the daily number of births at this
An industrial product is shipped in lots of 20. Testing to determine whether an item is defective is costly; hence, the manufacturer samples production rather than using a 100% inspection plan. The
24. Horse Kicks Ladislaus Bortkiewicz was a Russian economist and statistician who published a book entitled “The Law of Small Numbers.” In his book he showed that the number of soldiers in the
23. E. coli Outbreaks An outbreak of E. coli infections in July of 2017 occurred in southwestern Utah, with a dozen people sick, and the confirmed deaths of two children. E. coli infections and
22. Bacteria in Water Samples If a drop of water is examined under a microscope, the number x of a specific type of bacteria present has been found to have a Poisson probability distribution. Suppose
21. Accident Prone, continued Refer to Exercise 20.a. Calculate the mean and standard deviation for x, the number of injuries per year sustained by a schoolage child.b. Within what limits would you
20. Accident Prone According to a study conducted by the Department of Pediatrics at the University of California, San Francisco, children who are injured two or more times tend to sustain these
19. Intensive Care The number x of people entering the intensive care unit at a particular hospital on any one day has a Poisson probability distribution with mean equal to five persons per daya.
18. Airport Safety The increased number of small commuter planes in major airports has heightened concern over air safety. An eastern airport has recorded a monthly average of five near misses on
17. Flu Shots The probability that a person will develop the flu after getting a flu shot is 0.01. In a random sample of 200 people in a community who got a flu shot, what is the probability that 5
Let x be a Poisson random variable, find the probabilities for x using the Poisson formula. 5. =2; Px=0), P(x=1), P(x>1), and P(x = 5).
2. Based on your estimate of m, what is the estimated standard deviation of the number of cancer cases statewide? How safe is it to live near a nuclear reactor? Men who lived in a coastal strip that
22. Do You Return Your Questionnaires? A public opinion research firm claims that approximately 70% of those sent questionnaires respond by returning the questionnaire.Twenty such questionnaires are
21. The Triangle Test A procedure often used to control the quality of name-brand food products utilizes a panel of five “tasters.” Each member of the panel tastes three samples, two of which are
20. Conservative Spenders A USA Today snapshot shows that 60% of consumers say they have become more conservative spenders. When asked “What would you do first if you won $1 million tomorrow?”the

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