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Introduction To Probability And Statistics 14th Edition William Mendenhall, Robert Beaver, Barbara Beaver - Solutions
Assume that the chest measurements in Exercise 6.90 are normally distributed with a mean of µ = 39.83 and standard deviation of σ = 2.05.a. What proportion of the observations would lie between 36.5 and 43.5 inches?b. Between what two measurements would 95% of the observations lie?c. What are the
In Exercise 1.67, Allen Shoemaker derived a distribution of human body temperatures, which has a distinct mound-shape. Suppose we assume that the temperatures of healthy humans is approximately normal with a mean of 98.6 degrees and a standard deviation of 0.8 degrees. a. If a healthy person is
A Snapshot in USA Today indicates that 51% of Americans say the average person is not very considerate of others when talking on a cellphone.11 Suppose that 100 Americans are randomly selected. Find the approximate probability that 60 or more Americans would indicate that the average person is not
Philatelists (stamp collectors) often buy stamps at or near retail prices, but, when they sell, the price is considerably lower. For example, depending on the mix of a collection, condition, demand, economic conditions, etc., a collection may sell at x% of the retail price, where x is normally
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 examination scored
Although faculty salaries at colleges and universities in the United States continue to rise, they do not always keep pace with the cost of living and with salaries in the private sector. In 2010, the National Center for Educational Statistics indicated that the average salary for Assistant
Briggs and King developed the technique of nuclear transplantation, in which the nucleus of a cell from one of the later stages of the development of an embryo is transplanted into a zygote (a single-cell fertilized egg) to see whether the nucleus can support normal development. If the probability
Very often, at the end of an exam that seemed particularly difficult, students will ask the professor, "Are you going to curve the grades?" Unfortunately, "curving the grades" doesn't necessarily mean that you will receive a higher grade on a test, although you might like to think so! Curving
A population consists of N = 500 experimental units. Use a random number table to select a random sample of n = 20 experimental units. What is the probability that each experimental unit is selected for inclusion in the sample?
Does the race of an interviewer matter? This question was investigated by Chris Gilberg and colleagues and reported in an issue of Chance magazine. 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.
The American Journal of Human Biology reported on a study of a dietary assessment tool for use in the population of urban Native American youth. The subjects were Native American youth attending an after-school program in Minneapolis, MN. All 61 children between the ages of 9 and 13 who satisfied
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 class. a. Provide a randomization
Two different Gallup Polls were conducted for CNN/USA Today, both of which involved people's feelings about the U.S. space program. Here is a question from each poll, along with the responses of the sampled Americans:a. Read the two poll questions. Which of the two wordings is more unbiased?
Random samples of size n were selected from populations with the means and variances given here. Find the mean and standard deviation of the sampling distribution of the sample mean in each case: a. n = 36, µ = 10, σ2 = 9 b. n = 100, µ = 5, σ2 = 4 c. n = 8, µ = 120, σ2 = 1
Refer to Exercise 7.15. a. If the sampled populations are normal, what is the sampling distribution of for parts a, b, and c? b. According to the Central Limit Theorem, if the sampled populations are not normal, what can be said about the sampling distribution of for parts a, b, and c? Exercise
A population consists of N = 5 numbers: 1, 3, 5, 6, and 7. It can be shown that the mean and standard deviation for this population are µ = 4.4 and σ = 2.15, respectively.a. Construct a probability histogram for this population.b. Use the random number table, Table 10 in Appendix
Refer to Exercise 7.17. a. Use the data entry method in your calculator to find the mean and standard deviation of the 50 values of given in Exercise 7.17, part c. b. Compare the values calculated in part a to the theoretical mean m and the theoretical standard deviation σ/ √n for the sampling
A random sample of n observations is selected from a population with standard deviation σ = 1. Calculate the standard error of the mean (SE) for these values of n: a. n = 1 b. n = 2 c. n = 4 d. n = 9 e. n = 16 f. n = 25 g. n = 100 Plot the standard error of the mean (SE) versus the sample size n
A random sample of size n = 49 is selected from a population with mean µ = 53 and standard deviation σ = 21. a. What will be the approximate shape of the sampling distribution of ? b. What will be the mean and standard deviation of the sampling distribution of ?
Refer to Exercise 7.21. Find the probability that the sample mean is greater than 55.Exercise 7.21A random sample of size n = 49 is selected from a population with mean µ = 53 and standard deviation σ = 21.
A random sample of size n = 40 is selected from a population with mean µ = 100 and standard deviation σ = 20. a. What will be the approximate shape of the sampling distribution of ? b. What will be the mean and standard deviation of the sampling distribution of ?
Refer to Exercise 7.23. Find the probability that the sample mean is between 105 and 110.Exercise 7.23A random sample of size n = 40 is selected from a population with mean µ = 100 and standard deviation σ = 20.
Suppose a random sample of n = 25 observations is selected from a population that is normally distributed with mean equal to 106 and standard deviation equal to 12.a. Give the mean and the standard deviation of the sampling distribution of the sample mean .b. Find the probability that exceeds
Suppose that college faculty with the rank of professor at public 2-year institutions earn an average of $71,802 per year with a standard deviation of $4000. In an attempt to verify this salary level, a random sample of 60 professors was selected from a personnel database for all 2-year
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 chemical experiment that
Explain why the weight of a package of one dozen tomatoes should be approximately normally distributed if the dozen tomatoes represent a random sample.
Use the Central Limit Theorem to explain why a Poisson random variable-say, the number of a particular type of bacteria in a cubic foot of water-has a distribution that can be approximated by a normal distribution when the mean µ is large.
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 strength measurements
The normal daily human potassium requirement is in the range of 2000 to 6000 milligrams (mg), with larger amounts required during hot summer weather. The amount of potassium in food varies, but bananas are often associated with high potassium, with approximately 422 mg in a medium-sized banana.
The total daily sales, x, in the deli section of a local market is the sum of the sales generated by a fixed number of customers who make purchases 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
In Exercise 1.67, Allen Shoemaker derived a distribution of human body temperatures with a distinct mound shape. Suppose we assume that the temperatures of healthy humans are approximately normal with a mean of 98.6o and a standard deviation of 0.8o.a. If 130 healthy people are selected at random,
Sports that involve a significant amount of running, jumping, or hopping put participants at risk for Achilles tendinopathy (AT), an inflammation and thickening of the Achilles tendon. A study in The American Journal of Sports Medicine looked at the diameter (in mm) of the affected and non affected
Random samples of size n were selected from binomial populations with population parameters p given here. Find the mean and the standard deviation of the sampling distribution of the sample proportion in each case: a. n = 100, p = .3 b. n = 400, p = .1 c. n = 250, p = .6
Is it appropriate to use the normal distribution to approximate the sampling distribution of in the following circumstances? a. n = 50, p = .05 b. n = 75, p = .1 c. n = 250, p = .99
Random samples of size n = 75 were selected from a binomial population with p = .4. Use the normal distribution to approximate the following probabilities:a. P( ≤ .43)b. P(.35 ≤ ≤ .43)
Random samples of size n = 500 were selected from a binomial population with p = .1.a. Is it appropriate to use the normal distribution to approximate the sampling distribution of ? Check to make sure the necessary conditions are met. Using the results of part a, find these probabilities:b. >
Calculate SE() for n = 100 and these values of p: a. p = .01 b. p = .10 c. p = .30 d. p = .50 e. p = .70 f. p = .90 g. p = .99 h. Plot SE() 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 a
A random sample of size n = 50 is selected from a binomial distribution with population proportion p = .7.a. What will be the approximate shape of the sampling distribution of ?b. What will be the mean and standard deviation (or standard error) of the sampling distribution of ?c. Find the
A random sample of size n = 80 is selected from a binomial distribution with population proportion p = .25.a. What will be the approximate shape of the sampling distribution of ?b. What will be the mean and standard deviation (or standard error) of the sampling distribution of ?c. Find the
a. Is the normal approximation to the sampling distribution of appropriate when n = 400 and p = .8?b. Use the results of part a to find the probability that is greater than .83.c. Use the results of part a to find the probability that lies between .76 and .84.
Recycling trash, reducing waste, and reusing materials are eco-actions that will help the environment. According to a USA Today snapshot (Exercise 6.45), 78% of respondents list recycling as the leading way to help our environment. Suppose that a random sample of n = 100 adults is selected and that
Parents with children list a GPS system (28%) and a DVD player (28%) as "must have" accessories for a road trip. Suppose a sample of n = 1000 parents are randomly selected and asked what devices they would like to have for a family road trip. Let ^p be the proportion of parents in the sample who
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
It seems that driving with a pet in the car is the third worst driving distraction, behind talking on the phone and texting.According to an American Automobile Association study, 80% of drivers admit to driving with a pet in the car, and of those, 20% allow their dogs to sit on their laps. Suppose
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. They are less enthusiastic about the taste of mint or coffee that provide more
a. Use the data to determine the upper and lower control limits for an chart.b. What is the purpose of an chart?c. Construct an chart for the process and explain how it can be used.
a. Use the data to determine the upper and lower control limits for an chart.b. Construct an chart for the process and explain how it can be used.
Explain the difference between an chart and a p chart.
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. a. Use the data to find the upper and lower control limits for a p chart. b. Construct a p chart for the process
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. a. Use the data to find the upper and lower control limits for a p chart. b. Construct a p chart for the process
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. Construct a control chart for the proportion of defectives in samples of 400 rivets. Explain how the
The manager of a building-supplies company randomly samples incoming lumber to see whether it meets quality specifications. From each shipment, 100 pieces of 2 × 4 lumber are inspected and judged according to whether they are first (acceptable) or second (defective) grade. The
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 and s = .07, respectively. Construct an chart for the process and explain
The data in the table are measures of the radiation in air particulates at a nuclear power plant. Four measurements were recorded at weekly intervals over a 26-week period. Use the data to construct an chart and plot the 26 values of . Explain how the chart can be used.
A hardwoods manufacturing plant has a production line designed to produce baseball bats weighing 32 ounces. During a period of time when the production process was known to be in statistical control, the average bat weight was found to be 31.7 ounces. The observed data were gathered from 50
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 willing to accept the 72%
A finite population consists of four elements: 6, 1, 3, 2.a. How many different samples of size n = 2 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
Refer to Exercise 7.60. Find the sampling distribution for if random samples of size n = 3 are selected without replacement. Graph the sampling distribution of . Exercise 7.60 A finite population consists of four elements: 6, 1, 3, 2.
Suppose a random sample of n = 5 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 .b. Find the probability that exceeds 1.3.c. Find the
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 1110.b. The
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 standard deviation of
Studies 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 biomass in 400
The safety requirements for hard hats worn by construction workers and others, established by the American National Standards Institute (ANSI), specify that each of three hats pass the following test. A hat is mounted on an aluminum head form. An 8-pound steel ball is dropped on the hat from a
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, and a control group that does
The results of a CBS News Poll concerning views on same-sex marriage and gay rights given in the table that follows show that there is no consensus on this issue among Americans.a. Is this an observational study or a planned experiment? b. Is there the possibility of problems in responses arising
A biology experiment was designed to determine whether sprouting radish seeds inhibit the germination of lettuce seeds. 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 seeds and 13 radish
A study of about n = 1000 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. a. Is this an observational study or a designed experiment? b. What problems might
Suppose a telephone company executive wishes to select a random sample of n = 20 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. Use the random number
The proportion of individuals with an Rh-positive blood type is 85%. You have a random sample of n = 500 individuals. a. What are the mean and standard deviation of , the sample proportion with Rh-positive blood type? b. Is the distribution of approximately normal? Justify your answer. c. What
What survey design is used in each of these situations? a. A random sample of n = 50 city blocks is selected, and a census is done for each single-family dwelling on each block. b. The highway patrol stops every 10th vehicle on a given city artery between 9:00 A.M. and 3:00 P.M. to perform a
The maximum load (with a generous safety factor) for the elevator in an office building is 2000 pounds. The relative frequency distribution of the weights of all men and women using the elevator is mound-shaped (slightly skewed to the heavy weights), with mean µ equal to 150 pounds and standard
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 8-hour day? b. Do
Refer to Exercise 7.75. 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 1280 wiring packages per
The table lists the number of defective 60-watt light-bulbs found in samples of 100 bulbs selected over 25 days from a manufacturing process. Assume that during this time the manufacturing process was not producing an excessively large fraction of defectives.a. Construct a p chart to monitor the
A hardware store chain purchases large shipments of light-bulbs from the manufacturer described in Exercise 7.77 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 store's specifications
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.
During long production runs of canned tomatoes, the average weights (in ounces) of samples of five cans of standard- grade tomatoes in pureed form were taken at 30 control points during an 11-day period. These results are shown in the table. When the machine is performing normally, the average
An experimenter wants to find an appropriate temperature at which to store fresh strawberries to minimize the loss of ascorbic acid. There are 20 storage containers, each with controllable temperature, in which strawberries can be stored. If two storage temperatures are to be used, how would the
A bottler of soft drinks packages cans in six-packs. Suppose that the fill per can has an approximate normal distribution with a mean of 12 fluid ounces and a standard deviation of 0.2 fluid ounces. a. What is the distribution of the total fill for a case of 24 cans? b. What is the probability that
Packages of food whose average weight is 16 ounces with a standard deviation of 0.6 ounces 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 392 ounces (24.5 pounds)?
A manufacturing process is designed to produce an electronic component for use in small portable television sets. The components are all of standard size and need not conform to any measurable characteristic, but are sometimes inoperable when emerging from the manufacturing process. Fifteen samples
Contrary to current thought about omega-3 fatty acids, new research shows that the beneficial 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
The technique of simulating a process that contains random elements and repeating the process over and over to see how it behaves is called a Monte Carlo procedure. It is widely used in business and other fields to investigate the properties of an operation that is subject to random effects, such
Explain what is meant by "margin of error" in point estimation.
Suppose you are writing a questionnaire for a sample survey involving n = 100 individuals. The questionnaire will generate estimates for several different binomial proportions. If you want to report a single margin of error for the survey, which margin of error from Exercise 8.9 is the correct one
Partly because of our addiction to fast food, the average American consumes 32.7 pounds of cheese, 14.0 pounds of ice cream, and drinks 48.8 gallons of soda each year, according to the 2010 Statistical Abstract of the United States. Suppose that we test the accuracy of these reported averages by
Even though we know it may not be good for us, many Americans really enjoy their fast food! A survey conducted by Pew Research Center graphically illustrated our penchant for eating out, and in particular, eating fast food:a. This survey was based on "telephone interviews conducted with a
In an article in the Annals of Botany, a researcher reported the basal stem diameters of two groups of dicot sunflowers: those that were left to sway freely in the wind and those that were artificially supported. A similar experiment was conducted for monocot maize plants. Although the authors
In a regular NBA season, each team plays 82 games, some at home and some on the road. Can you afford the price of a ticket? The Web site wiki.answers.com indicates that the low prices are around $10 for the high up seats while the court-side seats are around $2000 to $5000 per game and that the
A dean of men wishes to estimate the average cost of the freshman year at a particular college correct to within $500, with a probability of .95. If a random sample of freshmen is to be selected and each asked to keep financial data, how many must be included in the sample? Assume that the dean
A quality-control engineer wants to estimate the fraction of defectives in a large lot of printer ink cartridges. From previous experience, he feels that the actual fraction of defectives should be somewhere around .05. How large a sample should he take if he wants to estimate the true fraction to
Samples of 400 printed circuit boards were selected from each of two production lines A and B. Line A produced 40 defectives, and line B produced 80 defectives. Estimate the difference in the actual fractions of defectives for the two lines with a confidence coefficient of .90.
Refer to Exercise 8.106. Suppose 10 samples of n = 400 printed circuit boards were tested and a confidence interval was constructed for p for each of the 10 samples. What is the probability that exactly one of the intervals will not contain the true value of p? That at least one interval will not
G. Wayne Marino investigated some of the variables related to "fast starts," the acceleration and speed of a hockey player from a stopped position. Sixty-nine hockey players, varsity and intramural, from the University of Illinois were included in the experiment. Each player was required to move as
Exercise 8.108 presented statistics from a study of fast starts by ice hockey skaters. The mean and standard deviation of the 69 individual average acceleration measurements over the 6-meter distance were 2.962 and .529 meters per second, respectively. a. Find a 95% confidence interval for this
A random sample of n = 900 observations from a binomial population produced x = 655 successes. Estimate the binomial proportion p and calculate the margin of error.
The mean and standard deviation of the speeds of the sample of 69 skaters at the end of the 6-meter distance in Exercise 8.108 were 5.753 and .892 meters per second, respectively. a. Find a 95% confidence interval for the mean velocity at the 6-meter mark. Interpret the interval. b. Suppose you
In addition to teachers and administrative staff, schools also have many other employees, including bus drivers, custodians, and cafeteria workers. In Auburn, WA, the average hourly wage is $16.92 for bus drivers, $17.65 for custodians, and $12.86 for cafeteria workers. Suppose that a second school
An experimental rehabilitation technique was used on released convicts. It was shown that 79 of 121 men subjected to the technique pursued useful and crime-free lives for a 3-year period following prison release. Find a 95% confidence interval for p, the probability that a convict subjected to the
If 36 measurements of the specific gravity of aluminum had a mean of 2.705 and a standard deviation of .028, construct a 98% confidence interval for the actual specific gravity of aluminum.
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