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

14. Lightbulbs, continued A hardware store chain purchases large shipments of lightbulbs from the manufacturer described in Exercise 13 and specifies that each shipment must contain no more than 4% defectives.When the manufacturing process is in control, what is the probability that the hardware
12. Wiring Packages, continued Refer to Exercise 11.Suppose the company employs 10 assemblers of wiring packages.a. Find the mean and standard deviation of the company’s daily (8-hour day) production of wiring packages.b. What is the probability that the company’s daily production is less than
11. Wiring Packages The number of wiring packages that can be assembled by a company’s employees has a normal distribution, with a mean equal to 16.4 per hour and a standard deviation of 1.3 per hour.a. What are the mean and standard deviation of the number x of packages produced per worker in an
10. Rh Positive The proportion of individuals with an Rh-positive blood type is 85%. You have a random sample of n5500 individuals.a. What are the mean and standard deviation of ˆp, the sample proportion with Rh-positive blood type?b. Is the distribution of ˆp approximately normal? Justify your
9. Telephone Service Suppose a telephone company executive wishes to select a random sample of n520 out of 7000 customers for a survey of customer attitudes concerning service. If the customers are numbered for identification purposes, indicate the customers whom you will include in your sample.
8. 9/11 A study of about n51000 individuals in the United States during September 21–22, 2001, revealed that 43% of the respondents indicated that they were less willing to fly following the events of September 11, 2001.23a. Is this an observational study or a designed experiment?b. What problems
7. Sprouting Radishes A biology experiment was designed to determine whether sprouting radish seeds inhibit the germination of lettuce seeds.22 Three 10-centimeter Petri dishes were used. The first contained 26 lettuce seeds, the second contained 26 radish seeds, and the third contained 13 lettuce
5. Biomass Studies20 indicate that the earth’s vegetative mass, or biomass for tropical woodlands, thought to be about 35 kilograms per square meter (kg/m2 ), may in fact be too high and that tropical biomass values vary regionally—from about 5 to 55 kg/m2. Suppose you measure the tropical
4. Lead Pipes Studies indicate that drinking water supplied by some old lead-lined city piping systems may contain harmful levels of lead. An important study of the Boston water supply system showed that the distribution of lead content readings for individual water specimens had a mean and
3. Suppose a random sample of n55 observations is selected from a population that is normally distributed, with mean equal to 1 and standard deviation equal to .36.a. Give the mean and standard deviation of the sampling distribution of x .b. Find the probability x that exceeds 1.3.c. Find the
2. Refer to Exercise 1. Find the sampling distribution for x if random samples of size n53 are selected without replacement. Graph the sampling distribution of x .
1. A finite population consists of four elements: 6, 1, 3, 2.a. How many different samples of size n52 can be selected from this population if you sample without replacement? (Sampling is said to be without replacement if an element cannot be selected twice for the same sample.)b. List the possible
16. Electronic Components A manufacturing process is designed to produce an electronic component for use in small portable tablets. The components are all of standard size and need not conform to any measurable characteristic, but are sometimes inoperable when emerging from the manufacturing
13. Baseball Bats A hardwoods manufacturing plant has a production line designed to produce baseball bats weighing 900 grams. During a period of time when the production process was known to be in statistical control, the average bat weight was found to be 892 grams.The observed data were gathered
11. Coal-Burning Power Plant A coal-burning power plant tests and measures three specimens of coal each day to monitor the percentage of ash in the coal. The overall mean of 30 daily sample means and the combined standard deviation of all the data were x 57.24 and s5.07, respectively.a. Construct
9. Brass Rivets A producer of brass rivets randomly samples 400 rivets each hour and calculates the proportion of defectives in the sample. The mean sample proportion calculated from 200 samples was equal to .021.a. Construct a control chart for the proportion of defectives in samples of 400
8. Black Jack A gambling casino records and plots the mean daily gain or loss from five blackjack tables on an x chart. The overall mean of the sample means and the standard deviation of the combined data over 40 weeks were x 5$10,752 and s5$1605, respectively.a. Construct an x chart for the mean
7. Samples of n=200 items were selected hourly over a 100-hour period, and the sample proportion of defectives was calculated each hour. The mean of the 100 sample proportions was .041. determine the upper and lower control limits for a p chart. Construct the control chart and explain how it can be
6. Samples of n=100 items were selected hourly over a 100-hour period, and the sample proportion of defectives was calculated each hour. The mean of the 100 sample proportions was .035. determine the upper and lower control limits for a p chart. Construct the control chart and explain how it can be
5. The sample means were calculated for 40 samples of size n55 for a process that was judged to be in control.The means of the 40 values and the standard deviation of the combined 200 measurements were x 5155.9 and s54.3, respectively. determine the upper and lower control limits for an x chart.
4. The sample means were calculated for 30 samples of size n510 for a process that was judged to be in control. The means of the 30 x -values and the standard deviation of the combined 300 measurements were x 520.74 and s5.87, respectively. determine the upper and lower control limits for an x
3. Explain the difference between an x chart and a p chart.
2. What is the purpose of a p chart?
1. What is the purpose of an x chart?
A manufacturer of ballpoint pens randomly samples 400 pens per day and tests each to see whether the ink flow is acceptable. The proportions of pens judged defective each day over a 40-day period are listed in Table 7.7. Construct a control chart for the proportion ˆp defective in samples of n5400
The inside diameter x of a particular type of bearing is a continuous random variable with an approximate mound-shaped distribution. A statistical process control monitoring system samples the inside diameters of n=4 bearings each hour for k=25 hours (see Table 7.6)Construct an x chart for
35. Oh, Nuts! Are you a chocolate “purist,” or do you like other ingredients in your chocolate? American Demographics reports that almost 75% of consumers like traditional ingredients such as nuts or caramel in their chocolate.17 A random sample of 200 consumers is selected and the number who
33. M&M’S An advertiser claims that the average percentage of brown M&M’S candies in a package of milk chocolate M&M’S is 13%. Suppose you randomly select a package of milk chocolate M&M’S that contains 55 candies and determine the proportion of brown candies in the package.a. What is the
30. Automated Vehicles From driverless cars to a workplace staffed by robots, automation has the potential to reshape many facets of American life. The large majority of Americans (87%) would favor a requirement that all driverless vehicles have a human in the driver’s seat who can take control
29. Walking while Talking A USA Today snapshot reports that approximately 23% of cell phone owners walked into someone or something while they were talking on their cell phone.12 In a random sample of n5200 cell phone owners, what is the probability that the sample proportion of cell phone owners
28. O Canada! The National Hockey League has approximately 70% of its players born outside the United States.11 In a random sample of n550 NHL players, what is the probability that the sample proportion of players born outside the United States exceeds 80%?
27. Tossing Coins A fair coin is tossed n580 times. Let ˆp be the sample proportion of heads. Find P(.44 , pˆ , .61).
26. A random sample of size n=400 is selected from a binomial distribution with p5.8. Find the probability that the sample proportion ˆp is greater than .83. The probability that the sample proportion ˆp is between .76 and .84. describe the approximate shape of the sampling distribution of ˆp
25. A random sample of size n=80 is selected from a binomial distribution with p5.25. Find the probability that the sample proportion ˆp is between .18 and .44. describe the approximate shape of the sampling distribution of ˆp and calculate its mean and standard deviation (or standard error).
24. A random sample of size n=50 is selected from a binomial distribution with p5.7. Find the probability that the sample proportion ˆp is less than .8. describe the approximate shape of the sampling distribution of ˆp and calculate its mean and standard deviation (or standard error). Then
23. Plotting the Standard Error Refer to Exercises 16–22. Plot SE (pˆ) versus p on graph paper and sketch a smooth curve through the points. For what value of p is the standard deviation of the sampling distribution of ˆp a maximum? What happens to the standard error when p is near 0 or near
Refer to Example 7.10. Suppose someone claims that the proportion p of parents in the population is actually equal to .55. What is the probability of observing a sample proportion as large as or larger than the observed value pˆ 5.60?
In a survey, 500 parents were asked about the importance of sports for boys and girls. Of the parents interviewed, 60% agreed that boys and girls should have equal opportunities to participate in sports. Describe the sampling distribution of the sample proportion ˆp of parents who agree that boys
33. Sports and Achilles Tendon Injuries Sports that involve a significant amount of running, jumping, or hopping put participants at risk for Achilles tendon injuries. A study in The American Journal of Sports Medicine looked at the diameter (in mm)of the injured and healthy tendons for patients
32. Normal Temperatures In Exercise 15 (Chapter 1 Review), Allen Shoemaker derived a distribution of human body temperatures with a distinct mound shape.9 Suppose we assume that the temperatures of healthy humans are approximately normal with a mean of 37.0°and a standard deviation of 0.4°.a. If
31. Deli Sales The total daily sales, S, in the deli section of a supermarket is the sum of the purchases made by customers on a given day.a. What kind of probability distribution do you expect the total daily sales to have? Explain.b. For this particular market, the average purchase per customer
30. Potassium Levels The amount of potassium in food varies, but bananas are often associated with high potassium, with approximately 422 mg in a medium-sized banana.8 Suppose the distribution of potassium in a banana is normally distributed, with mean equal to 422 mg and standard deviation equal
29. Paper Strength A paper manufacturer requires a minimum strength of 20 pounds per square inch. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour’s production and a strength measurement is recorded for each. Assume that the
28. Bacteria in Water Use the Central Limit Theorem to explain why a Poisson random variable—say, the number of a particular type of bacteria in a liter of water—has a distribution that can be approximated by a normal distribution when the mean m is large. (hint:One liter of water contains 1000
27. Tomatoes Explain why the weight of a package of one dozen tomatoes should be approximately normally distributed if the dozen tomatoes represent a random sample.
26. Measurement Error When research chemists perform experiments, they may obtain slightly different results on different replications, even when the experiment is performed identically each time. These differences are due to a phenomenon called “measurement error.”a. List some variables in a
25. Faculty Salaries Suppose that college faculty with the rank of professor at public 2-year institutions earn an average of $75,878 per year7 with a standard deviation of $4000. In an attempt to verify this salary level, a random sample of 60 professors was selected from an appropriate
24. Total Packing Weight Packages of food whose average weight is 450 grams with a standard deviation of 17 grams are shipped in boxes of 24 packages. If the package weights are approximately normally distributed, what is the probability that a box of 24 packages will weigh more than 11 kilograms?
23. Batteries A certain type of automobile battery is known to last an average of 1110 days with a standard deviation of 80 days. If 400 of these batteries are selected, find the following probabilities for the average length of life of the selected batteries:a. The average is between 1100 and
22. Cerebral Blood Flow Cerebral blood flow (CBF)in the brains of healthy people is normally distributed with a mean of 74 and a standard deviation of 16. A random sample of 25 stroke patients resulted in an average CBF of 69.7. If we assume that there is no difference between the CBF of healthy
21. O Baby! The weights of 3-month-old baby girls are normally distributed with a mean of 5.9 kilograms and a standard deviation of 0.7.6 In an inner city pediatric facility, a random sample of 16 3-month-old baby girls was selected and their weights were recorded.a. What is the probability that
20. Refer to Exercise 17.a. Find the probability that x exceeds 110.b. Find the probability that the sample mean deviates from the population mean m 5106 by no more than 4. calculate the probabilities
19. Refer to Exercise 16 and find the probability that the sample mean is between 105 and 110. calculate the probabilities
18. Refer to Exercise 15 and find the probability that the sample mean is greater than 55. calculate the probabilities
17. A random sample of size n=25 is selected from a normal population with mean m =106 and standard deviation s =12. describe the approximate shape of the sampling distribution for the sample mean and find its mean and standard error.
16. A random sample of size n=40 is selected from a population with mean m =100 and standard deviation s =20. describe the approximate shape of the sampling distribution for the sample mean and find its mean and standard error.
15. A random sample of size n=49 is selected from a population with mean m =53 and standard deviation s =21. describe the approximate shape of the sampling distribution for the sample mean and find its mean and standard error.
14. Refer to Exercises 7–13. Plot the standard error of the mean (SE) versus the sample size n and connect the points with a smooth curve. What is the effect of increasing the sample size on the standard error?
To determine whether a bottling machine is working satisfactorily, a production line manager randomly samples ten 12-ounce bottles every hour and measures the amount of beverage in each bottle. The mean x of the 10 fill measurements is used to decide whether to readjust the amount of beverage
The duration of Alzheimer’s disease from the time symptoms first appear until death ranges from 3 to 20 years; the average is 8 years with a standard deviation of 4 years. The administrator of a large medical center randomly selects the medical records of 30 deceased Alzheimer’s patients from
A population consists of N = 5 items—two of which are considered “successes”(S1 and S2) and three of which are considered “failures”(F1, F2, and F3 ). A random sample of n=2 items is selected, without replacement. 12. Find the sampling distribution for the sample proportion and display it
A population consists of N = 5 items—two of which are considered “successes”(S1 and S2) and three of which are considered “failures”(F1, F2, and F3 ). A random sample of n=2 items is selected, without replacement. 11. For each of the samples in Exercise 10, find the proportion of
A population consists of N = 5 items—two of which are considered “successes”(S1 and S2) and three of which are considered “failures”(F1, F2, and F3 ). A random sample of n=2 items is selected, without replacement. 10. List the possible samples that can be selected
A population consists of N =4 numbers:10, 15, 21, 22 with a mean of m =17. A random sample of n=2 is selected in one of two ways: first, without replacement and second, with replacement. 9. Find the mean of x for each of the distributions in Exercises 7 and 8. How do they compare with the
A population consists of N =4 numbers:10, 15, 21, 22 with a mean of m =17. A random sample of n=2 is selected in one of two ways: first, without replacement and second, with replacement. 8. How many possible random samples are available when sampling with replacement? List the possible samples.
A population consists of N =4 numbers:10, 15, 21, 22 with a mean of m =17. A random sample of n=2 is selected in one of two ways: first, without replacement and second, with replacement. 7. How many possible random samples are there when sampling without replacement? List the possible samples.Find
A population consists of N =5 numbers:11, 12, 15, 18, 20. A random sample of size n=3 is selected without replacement 6. Find the sampling distribution of the sample variance, s2.
A population consists of N =5 numbers:11, 12, 15, 18, 20. A random sample of size n=3 is selected without replacement 5. Find the sampling distribution of the range, R.
A population consists of N =5 numbers:11, 12, 15, 18, 20. A random sample of size n=3 is selected without replacement 4. Find the sampling distribution of the sample median, m
A population consists of N =5 numbers:11, 12, 15, 18, 20. A random sample of size n=3 is selected without replacement 3. Find the sampling distribution of the sample mean, x
A population consists of N =6 numbers:1, 3, 4, 7, 10, 11. A random sample of size n=4 is selected without replacement. 2. Find the sampling distribution of the sample median, m.
A population consists of N =6 numbers:1, 3, 4, 7, 10, 11. A random sample of size n=4 is selected without replacement. 1. Find the sampling distribution of the sample mean, x .
A population consists of N 55 numbers: 3, 6, 9, 12, 15. If a random sample of size n53 is selected without replacement, find the sampling distributions for the sample mean x and the sample median m.
30. Imagery and Memory A research psychologist is planning an experiment to determine whether the use of imagery—picturing a word in your mind—affects people’s ability to memorize. He wants to use two groups of subjects: a group that memorizes a set of 20 words using the imagery technique,
29. Pepsi or Coke? The battle for consumer preference continues between Pepsi and Coke. How can you weigh in? There is a website where you can vote for one of these colas if you click on the link that says PAY CASH for your opinion. Explain why the respondents do not represent a random sample of
27. Tai Chi and Fibromyalgia A small new study shows that tai chi, an ancient Chinese practice of exercise and meditation, may relieve symptoms of chronic painful fibromyalgia. The study assigned 66 fibromyalgia patients to take either a 12-week tai chi class, or attend a wellness education
26. Poor Wording? In a Fox News Poll3 conducted by Pulse Opinion Research in the state of Delaware, 1000 likely voters were asked to answer the following questions.• All in all, would you rather have bigger government that provides more services or smaller government that provides fewer
25. Racial Bias? Does the race of an interviewer matter?This question was investigated and reported in an issue of Chance magazine.2 The interviewer asked, “Do you feel that affirmative action should be used as an occupation selection criteria?” with possible answers of yes or no.a. What
24. Omega-3 Fats New research shows that omega-3 fats may not help reduce second heart attacks in heart attack survivors. The study included 4837 men and women being treated for heart disease. The experimental group received an additional 400 mg of the fats daily.1 Suppose that this experiment was
23. Sex and Violence One question on a survey questionnaire is phrased as follows: “Don’t you agree that there is too much sex and violence during prime TV viewing hours?” Comment on possible problems with the responses to this question. Suggest a better way to pose the question.
22. DMV Lists In many states, lists of possible jurors are assembled from voter registration lists and Department of Motor Vehicles records of licensed drivers and car owners. In what ways might this list not cover certain sectors of the population adequately?
21. Parks and Recreation A questionnaire was mailed to 1000 registered municipal voters selected at random.Only 500 questionnaires were returned, and of the 500 returned, 360 respondents were strongly opposed to a surcharge proposed to support the city Parks and Recreation Department. Are you
20. Every 10th Person A random sample of public opinion in a small town was obtained by selecting every 10th person who passed by the busiest corner in the downtown area. Will this sample have the characteristics of a random sample selected from the town’s citizens? Explain.
19. You post a short survey on Facebook and publish the results based on the reported responses. Identify the problems that might arise in each of the situations described
18. A question on a voter survey asked, “Do you agree that the current administration is ‘soft on crime’?” Identify the problems that might arise in each of the situations described
17. Only 30% of a mailed survey are returned. However, over 90% of the surveys returned agree with a proposed zoning change. Identify the problems that might arise in each of the situations described
16. A random sample of n51000 taxpayers from the city of San Bernardino is selected by the Internal Revenue Service and their tax returns are audited. What survey design is used in each of the situations described
15. Every 10th tree in a managed slash pine plantation is checked for pine needle borer infestation. What survey design is used in each of the situations described
14. One hundred households in each of four city wards are surveyed concerning a pending city tax relief referendum. What survey design is used in each of the situations described
13. The highway patrol stops every 10th vehicle on a given city street between 9:00 a.m. and 3:00 p.m. to perform a routine traffic safety check. What survey design is used in each of the situations described
12. A random sample of n550 city blocks is selected, and a census is done for each single-family dwelling on each block. What survey design is used in each of the situations described
11. A professor chooses the 20 students in his class whom he thinks will most likely return his questionnaire. identify the sampling plans as judgment, convenience, or quota sampling.
10. A population consists of 40% women and 60%men. The researcher decides to choose a sample consisting of 20 women and 30 men. identify the sampling plans as judgment, convenience, or quota sampling.
9. A student waits until Sunday night to complete a survey for his sociology class. He asks 10 of his fraternity brothers to participate. identify the sampling plans as judgment, convenience, or quota sampling.
8. A doctor chooses six of his most “at risk” patients to participate in a clinical trial. identify the sampling plans as judgment, convenience, or quota sampling.
7. A store manager randomly selects 10 sales receipts from each of the store’s six departments. identify the sampling plans as either cluster, stratified, or 1-in-k systematic samples.
6. An auditor selects every 100th entry in a ledger for amount verification. identify the sampling plans as either cluster, stratified, or 1-in-k systematic samples.
5. Ten homes are randomly selected and all adult occupants are surveyed. identify the sampling plans as either cluster, stratified, or 1-in-k systematic samples.
4. Select n510 drivers from a DMV database containing 20,000 drivers. use the random number table to identify the experimental units to be included in a simple random sample
3. Select n515 voters from a population of 50, 000 voters. use the random number table to identify the experimental units to be included in a simple random sample

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