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Introduction To Probability And Statistics 15th Edition William Mendenhall Iii , Robert Beaver , Barbara Beaver - Solutions

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 standard deviation of .45%.a. What is the probability that a particular state would have more than 2% of
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 calisthenics.However, the top recreational activity for men was still the relaxing sport of fishing,
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 temperatures of healthy humans is approximately normal with a mean of 37.0 degrees and a standard deviation of
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 standard deviations, did your score depart from the mean?b. What percentage of those who took the
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 people will have CBF readings between 60 and 80?
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 people will have CBF readings above 100?
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 below 40, he is classified as at risk for a stroke. What proportion of healthy people will mistakenly
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 guaranteed for a period of 5 years, what fraction will need to be repaired and/or replaced?
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 should the test be terminated if you wish to allow sufficient time for 90% of the students to complete
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, give the setting for m so that 8-ounce cups will overflow only 1% of the time.
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 distributed.a. Find the upper and lower quartiles for the gestation times.b. Would it be unusual to
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 the highest 15% as extroverts, what would be the proper score to choose as the cutoff point?
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 weights of these “1-pound” packages are normally distributed with a mean of 1.00 pound and a
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 elected from 1789 through 2016, 19 were 1.83 m or taller.2 Would you consider this to be unusual,
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 Trump is 1.88 m. Is this an unusual height?
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, find and .
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 deviation of 0.7.1 Use this information to answer 46. What proportion of 3-month-old baby girls will weigh
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 deviation of 0.7.1 Use this information to answer 47. What is the probability that a 3-month-old baby boy
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 deviation of 0.7.1 Use this information to answer 48. Would it be unusual to find a 3-month-old baby boy
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 all men will be taller than 1.83 meters? (hint: Convert the measurements to centimeters.)
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 probability that a randomly selected man will be between 1.73 m and 1.85 m tall?
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 of the trees will have diameters between 7.5 and 12.5 centimeters?b. What proportion of the trees
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 meters. Suppose you are traveling 65 km/h in a residential area and a car moves abruptly into your path
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. On what proportion of days will the daily discharge exceed 50 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 = 25 and p=.3
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 = 15 and p = .5
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. 5. P(x >9) when n=25 and p=.6
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. 6. P(6x9) when n=25 and p=.3
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. 7. P(20 < x < 25) when n=100 and p=.2
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. 8. P(x22) when n = 100 and p = .2
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. 9. P(x22) when n = 100 and p = .2
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. 10. P(x25) when n = 100 and p=.2
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. 11. P(355x360) when n=400 and p=.9
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 45 and p=.05
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 and p=.6
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 artificially supported.5 Suppose that the unsupported stem diameters at the base of a particular
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 forecasts is the consensus forecast. Suppose the individual 2017 January prime interest rate
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 and a standard deviation of 9. What is the probability that a given 1-ml sample will contain more
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 money on their purchases on Saturdays and Sundays! Suppose that the amount of money spent at shopping
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 that these pulse rates are approximately normally distributed with a mean of 78 and a standard
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 that the bearing diameter equal .500 inch6.004 inch, what fraction of the production will be
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 defectives were observed. Calculate the approximate probability of observing 27 or more defectives,
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 probability of observing 211 or fewer consumers who prefer her brand of soda
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 answers. 12. P(x 6) and P(x > 6) when n = 15 and p = .5
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 4 5 p(x).1 .3 .4 .1 ? .05
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 12. The probability of observing exactly two successes
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 11. The probability of observing no successes
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. The probability of observing at most two successes.
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. The probability of observing one success.
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. The probability of observing all successes.
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 13. The probability of observing at least two successes
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 selection for x50,1, 2, 3.
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 agree with Tchebysheff’s Theorem?
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 per minute?b. What is the probability that the number of visits per minute is less than or equal to
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 per 30 minutes?b. What is the probability distribution for the number of calls to this hotline per
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 during a given week?b. What is the probability that there will be at least one bankruptcy filing during a
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 approximation accurate? 11. Calculate P(x>6) when n=25 and p = .2.
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 approximation accurate? 10. Calculate p(0) and p(1) when n = 25 and p=.05.
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 approximation accurate? 9. Calculate P(x 2) when n = 20 and p=.1.
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 workrelated accidents at this site during a given week?b. What is the probability that there will be at
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 hospital?b. What is the probability distribution for the number of hourly births?c. What is the probability
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 sampling plan calls for sampling five items from each lot and rejecting the lot if more than one
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 Prussian cavalry killed by being kicked by a horse each year in each of 14 cavalry corps over a
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 outbreaks have been on the rise since 2009, reaching an incidence rate of 2.85 cases per 100,000
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 the maximum permissible count per water specimen for this type of bacteria is five. If the mean
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 expect the number of injuries per year to fall?
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 injuries during a relatively limited time, usually 1 year or less. If the average number of injuries per
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. What is the probability that the number of people entering the intensive care unit on a particular day
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 landings and takeoffs in the past 5 years.a. Find the probability that during a given month there are
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 or more of the 200 people will get the flu? Use the Poisson approximation to binomial probabilities
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 extends 32 kilometers north from a nuclear reactor in Plymouth, Massachusetts, developed some forms
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 sent out, and assume that the firm’s claim is correct.a. What is the probability that exactly 10
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 from batches of the product known to have the desired taste and the other from the latest batch.
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 answers had to do with somewhat conservative measures like “hire a financial adviser,” or

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