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introduction to probability statistics

Questions and Answers of Introduction To Probability Statistics

5.80 Problems with Your New Smartphone? A new study by Square Trade indicates that smartphones are 50% more likely to malfunction than simple phones over a three-year period.14 Of smartphone
5.79 Diabetes in Children Insulin-dependent diabetes (IDD) is a common chronic disorder of chil- dren. This disease occurs most frequently in persons of northern European descent, but the incidence
5.78 Football Coin Tosses During the 1992 football season, the Los Angeles Rams (now the St. Louis Rams) had a bizarre streak of coin-toss losses. In fact, they lost the call 11 weeks in a row. 12a.
5.77 Dominant Traits The alleles for black (B) and white (b) feather colour in chickens show incomplete dominance; individuals with the gene pair Bb have "blue" feathers. When one individual that is
5.76 Plant Genetics A peony plant with red petals was crossed with another plant having streaky petals. The probability that an offspring from this cross has red flowers is 0.75. Let X be the number
5.75 Plant Density One model for plant competi- tion assumes that there is a zone of resource depletion around each plant seedling. Depending on the size of the zones and the density of the plants,
5.74 What's for Breakfast? A packaging experiment is conducted by placing two different package designs for a breakfast food side by side on a supermarket shelf. The objective of the experiment is to
5.73 Probability of Rain Most weather forecasters protect themselves very well by attaching probabili- ties to their forecasts, such as "The probability of rain today is 40%." Then, if a particular
5.72 Grey Hair on Campus University campuses are greying! According to a recent article, one in four college students is aged 30 or older. Many of these students are women updating their job skills.
5.71 Student Fees A student union states that 80% of all students favour an increase in student fees to subsidize a new recreational area. A random sample of n = 25 students produced 15 in favour of
5.70 Psychosomatic Problems A psychiatrist believes that 80% of all people who visit doctors have problems of a psychosomatic nature. She decides to select 25 patients at random to test her theory.a.
5.69 Reality TV Reality TV (Survivor, Fear Factor, etc.) is a relatively new phenomenon in television programming, with contestants escaping to remote locations, taking dares, breaking world records,
5.68 Vacation Homes Approximately 60% of Canadians rank "owning a vacation home nestled on a beach or near a mountain resort" as their number one choice for a status symbol. A sample of n = 400
5.67 Income Splitting According to an Ipsos Reid survey (February 27, 2007), conducted on behalf of CanWest/Global News, most Canadians (77%) are in favour of "income splitting" for couples. 10
5.66 Integers II Refer to Exercise 5.65. Twenty people are asked to select a number from 0 to 9. Eight of them choose a 4, 5, or 6.a. If the choice of any one number is as likely as any other, what
5.65 Integers If a person is given the choice of an integer from 0 to 9, is it more likely that he or she will choose an integer near the middle of the sequence than one at either end?a. If the
5.64 Garbage Collection A city administrator claims that 80% of all people in the city favour garbage collection by contract to a private concern (in contrast to collection by city employees). To
5.63 Cancer Survivor Rates The 10-year survival rate for bladder cancer is approximately 50%. If 20 people who have bladder cancer are properly treated for the disease, what is the probability
5.62 Coins, continued Refer to Exercise 5.61. Suppose the coin is definitely unbalanced and the probability of a head is equal to p=0.1. Follow the instructions in partsa, b,c, andd. Note that the
5.61 Tossing a Coin A balanced coin is tossed three times. Let X equal the number of heads observed.a. Use the formula for the binomial probability distri- bution to calculate the probabilities
5.60 Under what conditions would you use the hypergeometric probability distribution to evaluate the probability of x successes in n trials?
5.59 Under what conditions can the Poisson ran- dom variable be used to approximate the probabilities associated with the binomial random variable? What application does the Poisson distribution have
5.58 List the five identifying characteristics of the binomial experiment.
5.57 Seed Treatments Seeds are often treated with a fungicide for protection in poor-draining, wet environments. In a small-scale trial prior to a large- scale experiment to determine what dilution
5.56 Teaching Credentials In Southern Ontario, a growing number of persons pursuing a teaching credential are choosing paid internships over traditional student teaching programs. A group of eight
5.55 Gender Bias? A company has five applicants for two positions: two women and three men. Suppose that the five applicants are equally qualified and that no pref- erence is given for choosing
5.54 Defective Computer Chips A piece of electronic equipment contains six computer chips, two of which are defective. Three computer chips are randomly chosen for inspection, and the number of
5.53 Candy Choices A candy dish contains five blue and three red candies. A child reaches up and selects three candies without looking.a. What is the probability that there are two blue and one red
5.52 Let X be a hypergeometric random variable with N=15, n=3, and M = 4.a. Calculate p(0), p(1), p(2), and p(3).b. Construct the probability histogram for x.c. Use the formulas given in Section 5.4
5.51 Let X be the number of successes observed in a sample of n = 5 items selected from N = 10. Suppose that, of the N = 10 items, 6 are considered "successes."a. Find the probability of observing no
5.50 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, 5 are considered "successes."a. Find the probability of
5.49 Evaluate these probabilities: Cic CC Cc a. b. C. C C
An eight-cylinder automobile engine has two misfiring spark plugs. The mechanic removes all four plugs from one side of the engine. What is the probability the two misfiring spark plugs are among
A rental truck agency services its vehicles on a regular basis, checking for mechanical problems. Suppose that the agency has six moving vans, two of which need to have new brakes. During a routine
A particular industrial product is shipped in lots of 20. Testing to determine whether each item is defective is costly; hence, the manufacturer samples production rather than using a 100% inspection
A case of wine has 12 bottles, 3 of which contain spoiled wine. A sample of 4 bottles is randomly selected from the case. 1. Find the probability distribution for X, the number of bottles of spoiled
5.48 E. coli Outbreak Increased research and discussion have focused on the number of illnesses involving the organism Escherichia coli (01257:H7), which causes a breakdown of red blood cells and
5.47 Bacteria in Water Samples If a drop of water is placed on a slide and examined under a micro- scope, the number X of a particular type of bacteria present has been found to have a Poisson
5.46 Cross-Border Drinking, continued Refer to Exercise 5.45.a. Calculate the mean and standard deviation for X, the number of fatalities per year.b. Within what limits would you expect the number of
5.45 Cross-Border Drinking Alcohol-related crashes increased in Windsor after bar hours extended, the Windsor Star reported in November 7, 2005. The number of injuries and fatalities from alcohol-
5.44 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 people per day.a.
5.43 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
5.42 Poisson vs. Binomial II To illustrate how well the Poisson probability distribution approxi- mates the binomial probability distribution, calculate the Poisson approximate values for p(0) and
5.41 Poisson vs. Binomial Let X be a binomial random variable with n = 20 and p=0.1.a. Calculate P(X 2) using Table 1 in Appendix I to obtain the exact binomial probability.b. Use the Poisson
5.40 Let X be a Poisson random variable with mean =2.5. Use Table 2 in Appendix I to calculate these probabilities:a. P(X5)b. P(X>6)c. P(X=2)d. P(1x4)
5.39 Let X be a Poisson random variable with mean => 2. Calculate these probabilities:a. P(X=0)c. P(X>1)b. P(X-1)d. P(X=5)
5.38 Consider a Poisson random variable X with 3. Use Table 2 in Appendix I to find the following probabilities:a. P(X 3)c. P(X=3)b. P(X>3)d. P(3x5)
5.37 Consider a Poisson random variable X with =3. Use the Poisson formula to calculate the following probabilities:a. P(X=0)b. P(X=1)c. P(X>1)
5.36 Consider a Poisson random variable X with =2.5. Use the Poisson formula to calculate the following probabilities:a. P(X=0)c. P(X=2)b. P(X=1)d. P(X 2)
A manufacturer of power lawn mowers buys one-horsepower, two-cycle engines in lots of 1000 from a supplier. She then equips each of the mowers produced by her plant with one of the engines. History
In 2001, an 82-year-old man in Ontario claimed that a convenience store clerk defrauded him of $250,000 by telling him that his ticket was not a winner and keeping it. The story received national
Suppose a life insurance company insures the lives of 5000 men aged 42. If actuarial studies show the probability that any 42-year-old man will die in a given year to be 0.001, find the exact
Refer to Example 5.11, where we calculated probabilities for a Poisson distribution with u=2 and =4. Use the cumulative Poisson table to find the probabilities of these events: 1. No accidents during
On February 7, 1976, Darryl Sittler scored 10 points in a hockey game while playing for the Toronto Maple Leafs. Wayne Gretzky has the most points of any hockey player in history, averaging 2.629
The average number of traffic accidents on a certain section of highway is two per week. Assume that the number of accidents follows a Poisson distribution with =2. 1. Find the probability of no
5.35 Less Vegetable Servings Many Canadians report consuming fewer servings of vegetables in the winter than in the summer, according to an Ipsos Reid/Campbell Company of Canada survey. Specifically,
5.34 Taste Test for PTC The taste test for PTC (phenylthiocarbamide) is a favourite exercise for every human genetics class. It has been established that a single gene determines the characteristic,
5.33 Fast Food and Gas Stations Forty percent of all Canadians who travel by car look for gas sta- tions and food outlets that are close to or visible from the highway. Suppose a random sample of n =
5.32 Pet Peeves Across the board, 22% of car leisure travellers rank "traffic and other drivers" as their pet peeve while travelling. Of car leisure travel- lers in the densely populated U.S.
5.31 Colour Preferences in Mice In a psychol- ogy experiment, a researcher plans to test the colour preference of mice under certain experimental condi- tions. She designs a maze in which the mouse
5.30 Whitefly Infestation Suppose that 10% of the fields in a given agricultural area are infested with the sweet potato whitefly. One hundred fields in this area are randomly selected and checked
5.29 Medical Bills II Consider the medical payment problem in Exercise 5.28 in a more realistic setting. Of all patients admitted to the clinic, 30% fail to pay their bills and the debts are
5.28 Medical Bills Records show that 30% of all patients admitted to an alternative medicine clinic fail to pay their bills and that eventually the bills are for- given. Suppose n=4 new patients
5.27 O Canada! The National Hockey League (NHL) has 80% of its players born outside the United States, and of those born outside the United States, 50% are born in Canada. Suppose that n = 12 NHL
5.26 Harry Potter Of all the Harry Potter books purchased in a recent year, about 60% were purchased for readers 14 or older. If 12 Harry Potter fans who bought books that year are surveyed, find the
5.25 Car Colours Car colour preferences change over the years and according to the particular model that the customer selects. In a recent year, 10% of all luxury cars sold were black. If 25 cars of
5.24 Blood Types In a certain population, 85% of the people have Rh-positive blood. Suppose that two people from this population get married. What is the probability that they are both Rh-negative,
5.23 Security Systems A home security system is designed to have a 99% reliability rate. Suppose that nine homes equipped with this system experience an attempted burglary. Find the probabilities of
5.22 MCAT Scores In 2006 the average com- bined MCAT score (physical science, verbal reason- ing, biological science) for students in Canada was 24.7. Suppose that approximately 45% of all students
5.19 Let X be a binomial random variable with n = 20 and p=0.1.a. Calculate P(X4) using the binomial formula.b. Calculate P(X 4) using Table 1 in Appendix I.c. Use the Excel output below to calculate
5.18 In Exercise 5.17, the mean and standard devia- tion for a binomial random variable were calculated for a fixed sample size, n = 100, and for different values of p. Graph the values of the
5.17 Find the mean and standard deviation for a binomial distribution with n = 100 and these values of p:a. p=0.01d. p=0.7b. p=0.9e. p=0.5c. p=0.3
5.16 Find the mean and standard deviation for a binomial distribution with these values:a. n = 1000, p = 0.3c. n=500, p=0.5b. n=400, p=0.01d. n 1600, p 0.8
5.15 Use Table 1 in Appendix I to find the following: a. P(X
5.14 Find P(X k) in each case:a. n=20, p=0.05, k=2b. n 15, p=0.7, k=8 -c. n 10, p=0.9, k=9
5.13 Use Table 1 in Appendix I to evaluate the following probabilities for n=6 and p=0.8:a. P(X4)c. P(X 1) Verify these answers using the values of p(x) calcu- lated in Exercise 5.9.
5.12 Use Table 1 in Appendix I to find the sum of the binomial probabilities from X=0 to X=k for these cases:a. n 10, p=0.1, k=3b. n 15, p=0.6, k=7c. n=25, p=0.5, k=14
5.11 Let X be a binomial random variable with n = 10 and p 0.4. Find these values:a. P(X=4)d. P(X 4)b. P(X4)c. P(X>4)e. = npf. = Vnpq
5.10 If X has a binomial distribution with p = 0.5, will the shape of the probability distribution be symmetric, skewed to the left, or skewed to the right?
5.8 Use the formula for the binomial probability distribution to calculate the values of p(x), and con- struct the probability histogram for X when n = 6 and p=0.2. [HINT: Calculate P(X=k) for seven
5.7 Let X be a binomial random variable with n = 7, p=0.3. Find these values:a. P(X=4)d. = npb. P(X 1)c. P(X>1)e. = Vnpq
5.6 Evaluate these binomial probabilities:a. C (0.2)(0.8)8c. C (0.2)(0.8)6b. C (0.2)(0.8)7d. P(X 1) when n = 8, p=0.2e. P(two or fewer successes)
5.5 Evaluate these binomial probabilities:a. C(0.3)(0.7)6b. C (0.05)(0.95)+c. C (0.5) (0.5)7d. C (0.2)(0.8)6
5.4 The Urn Problem, continued Refer to Exercise 5.3. Assume that the sampling was conducted with replacement. That is, assume that the first ball was selected from the jar, observed, and then
5.3 The Urn Problem A jar contains five balls: three red and two white. Two balls are randomly selected without replacement from the jar, and the number X of red balls is recorded. Explain why X is
5.2 Consider a binomial random variable with n = 9 and p=0.3. Let X be the number of successes in the sample.a. Find the probability that X is exactly 2.b. Find the probability that X is less than
5.1 Consider a binomial random variable with n = 8 and p=0.7. Let X be the number of successes in the sample.a. Find the probability that X is 3 or less.b. Find the probability that X is 3 or more.c.
Would you rather take a multiple-choice or a full recall test? If you have absolutely no knowledge of the material, you will score zero on a full recall test. However, if you are given five choices
- A regimen consisting of a daily dose of vitamin C was tested to determine its effective- ness in preventing the common cold. Ten people who were following the prescribed regimen were observed for a
Refer to Example 5.7 and the binomial random variable X with n = 5 and p=0.6. Use the cumulative binomial table in Table 5.1 to find the remaining binomial probabilities: p(0), p(1), p(2), p(4), and
Use the cumulative binomial table for n=5 and p=0.6 to find the probabilities of these events: 1. Exactly three successes 2. Three or more successes
Over a long period of time it has been observed that a given marksman can hit a target on a single trial with probability equal to 0.8. Suppose he fires four shots at the target. 1. What is the
Find P(X=2) for a binomial random variable with n = 10 and p = 0.1.
A patient fills a prescription for a 10-day regimen of two pills daily. Unknown to the pharmacist and the patient, the 20 tablets consist of 18 pills of the prescribed medica- tion and 2 pills that
Suppose there are approximately 1,000,000 adults in a city and an unknown proportion, p. favour term limits for politicians. A sample of 1000 adults will be chosen in such a way that every one of the
The Islamic calendar is lunar. The beginning and ending of the calendar are determined by the sighting of the crescent moon (new moon). Muslims are supposed to sight the crescent everywhere they
A poker hand consists of five cards from a deck of 52 ordinary cards. A player received five cards and did not look at them. Suppose that among these five cards, one card is the ace of spades, but
How to Use Table 2 to Calculate Poisson Probabilities
How to Use Table 1 to Calculate Binomial Probabilities
A box of condiments has ten small packages, in which three are ketchup, three are mustard, and four are relish. A sample of three packages is randomly selected (without replacement) from the box.a.

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