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business statistics in practice

The Practice Of Statistics 5th Edition Daren S. Starnes, Josh Tabor - Solutions

Men’s heights The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2.5 inches. Draw an accurate sketch of the distribution of men’s heights.Be sure to label the mean, as well as the points 1, 2, and 3 standard deviations away from
Potato chips The distribution of weights of 9-ounce bags of a particular brand of potato chips is approximately Normal with mean m = 9.12 ounces and standard deviation s = 0.05 ounce. Draw an accurate sketch of the distribution of potato chip bag weights. Be sure to label the mean, as well as the
Men’s heights Refer to Exercise 41. Use the 68–95–99.7 rule to answer the following questions. Show your work!(a) Between what heights do the middle 95% of men fall?(b) What percent of men are taller than 74 inches?(c) What percent of men are between 64 and 66.5 inches tall?(d) A height of
Potato chips Refer to Exercise 42. Use the 68–95–99.7 rule to answer the following questions. Show your work!(a) Between what weights do the middle 68% of bags fall?(b) What percent of bags weigh less than 9.02 ounces?(c) What percent of 9-ounce bags of this brand of potato chips weigh between
Estimating SD The figure below shows two Normal curves, both with mean 0. Approximately what is the standard deviation of each of these curves? - -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 80 1.2 1.6
A Normal curve Estimate the mean and standard deviation of the Normal density curve in the figure below. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Table A practice(a) z < 2.85 (c) z > −1.66(b) z > 2.85 (d) −1.66 < z < 2.85
Table A practice(a) z < −2.46 (c) 0.89 < z < 2.46(b) z > 2.46 (d) −2.95 < z < −1.27
More Table A practice(a) z is between −1.33 and 1.65(b) z is between 0.50 and 1.79
More Table A practice(a) z is between −2.05 and 0.78(b) z is between −1.11 and −0.32
Working backward(a) The 10th percentile.(b) 34% of all observations are greater than z.
Working backward(a) The 63rd percentile.(b) 75% of all observations are greater than z.
Length of pregnancies The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days.(a) At what percentile is a pregnancy that lasts 240 days(that’s about 8 months)?(b) What percent of
IQ test scores Scores on the Wechsler Adult Intelligence Scale (a standard IQ test) for the 20 to 34 age group are approximately Normally distributed with m = 110 and s = 25.(a) At what percentile is an IQ score of 150?(b) What percent of people aged 20 to 34 have IQs between 125 and 150?(c) MENSA
Put a lid on it! At some fast-food restaurants, customers who want a lid for their drinks get them from a large stack left near straws, napkins, and condiments.The lids are made with a small amount of flexibility so they can be stretched across the mouth of the cup and then snugly secured. When
I think I can! An important measure of the performance of a locomotive is its “adhesion,” which is the locomotive’s pulling force as a multiple of its weight.The adhesion of one 4400-horsepower diesel locomotive varies in actual use according to a Normal distribution with mean m = 0.37 and
Put a lid on it! Refer to Exercise 55. The supplier is considering two changes to reduce the percent of its large-cup lids that are too small to 1%. One strategy is to adjust the mean diameter of its lids. Another option is to alter the production process, thereby decreasing the standard deviation
I think I can! Refer to Exercise 56. The locomotive’s manufacturer is considering two changes that could reduce the percent of times that the train arrives late.One option is to increase the mean adhesion of the locomotive. The other possibility is to decrease the variability in adhesion from
Deciles The deciles of any distribution are the values at the 10th, 20th, . . . , 90th percentiles. The first and last deciles are the 10th and the 90th percentiles, respectively.(a) What are the first and last deciles of the standard Normal distribution?(b) The heights of young women are
Flight times An airline flies the same route at the same time each day. The flight time varies according to a Normal distribution with unknown mean and standard deviation. On 15% of days, the flight takes more than an hour. On 3% of days, the flight lasts 75 minutes or more. Use this information to
Brush your teeth The amount of time Ricardo spends brushing his teeth follows a Normal distribution with unknown mean and standard deviation.Ricardo spends less than one minute brushing his teeth about 40% of the time. He spends more than two minutes brushing his teeth 2% of the time. Use this
Sharks Here are the lengths in feet of 44 great white sharks:11 18.7 12.3 18.6 16.4 15.7 18.3 14.6 15.8 14.9 17.6 12.1 16.4 16.7 17.8 16.2 12.6 17.8 13.8 12.2 15.2 14.7 12.4 13.2 15.8 14.3 16.6 9.4 18.2 13.2 13.6 15.3 16.1 13.5 19.1 16.2 22.8 16.8 13.6 13.2 15.7 19.7 18.7 13.2 16.8(a) Enter these
Density of the earth In 1798, the English scientist Henry Cavendish measured the density of the earth several times by careful work with a torsion balance.The variable recorded was the density of the earth as a multiple of the density of water. Here are Cavendish’s 29 measurements:12 5.50 5.61
Runners’ heart rates The figure below is a Normal probability plot of the heart rates of 200 male runners after six minutes of exercise on a treadmill.13 The distribution is close to Normal. How can you see this? Describe the nature of the small deviations from Normality that are visible in the
Carbon dioxide emissions The figure below is a Normal probability plot of the emissions of carbon dioxide per person in 48 countries.14 In what ways is this distribution non-Normal?. Expected z-score -2 -3 1 3 2- 0 2 4 6 8 10 12 14 16 18 20 CO2 emissions (metric tons per person)
Is Michigan Normal? We collected data on the tuition charged by colleges and universities in Michigan.Here are some numerical summaries for the data:Mean Std. Dev. Min Max 10614 8049 1873 30823 Based on the relationship between the mean, standard deviation, minimum, and maximum, is it reasonable to
Weights aren’t Normal The heights of people of the same gender and similar ages follow Normal distributions reasonably closely. Weights, on the other hand, are not Normally distributed. The weights of women aged 20 to 29 have mean 141.7 pounds and median 133.2 pounds. The first and third
Two measures of center are marked on the density curve shown. Which of the following is correct?(a) The median is at the yellow line and the mean is at the red line.(b) The median is at the red line and the mean is at the yellow line.(c) The mode is at the red line and the median is at the yellow
Point C on this Normal curve corresponds to(a) 84 grams. (c) 78 grams. (e) 74 grams.(b) 82 grams. (d) 76 grams.
About what percent of the cockroaches have weights between 76 and 84 grams?(a) 99.7% (c) 68% (e) 34%(b) 95% (d) 47.5%
About what proportion of the cockroaches will have weights greater than 83 grams?(a) 0.0228 (c) 0.1587 (e) 0.0772(b) 0.0668 (d) 0.9332
A different species of cockroach has weights that follow a Normal distribution with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams. Based on this report, what is the approximate standard
The following Normal probability plot shows the distribution of points scored for the 551 players in the 2011–2012 NBA season.If the distribution of points was displayed in a histogram, what would be the best description of the histogram’s shape?(a) Approximately Normal (b) Symmetric but not
Gas it up! (1.3) Interested in a sporty car? Worried that it might use too much gas? The Environmental Protection Agency lists most such vehicles in its “two-seater” or “minicompact” categories. The figure shows boxplots for both city and highway gas mileages for our two groups of cars.
Python eggs (1.1) How is the hatching of water python eggs influenced by the temperature of the snake’s nest? Researchers assigned newly laid eggs to one of three temperatures: hot, neutral, or cold.Hot duplicates the extra warmth provided by the mother python, and cold duplicates the absence of
s Paul tall? According to the National Center for Health Statistics, the distribution of heights for 15-year-old males has a mean of 170 centimeters(cm) and a standard deviation of 7.5 cm. Paul is 15 years old and 179 cm tall.(a) Find the z-score corresponding to Paul’s height. Explain what this
Computer use Mrs. Causey asked her students how much time they had spent using a computer during the previous week. The following figure shows a cumulative relative frequency graph of her students’ responses.(a) At what percentile does a student who used her computer for 7 hours last week
Aussie, Aussie, Aussie A group of Australian students were asked to estimate the width of their classroom in feet. Use the dotplot and summary statistics below to answer the following questions.(a) Suppose we converted each student’s guess from feet to meters (3.28 ft = 1 m). How would the shape
What the mean means The figure below is a density curve. Trace the curve onto your paper.(a) Mark the approximate location of the median. Explain your choice of location.(b) Mark the approximate location of the mean. Explain your choice of location.
Horse pregnancies Bigger animals tend to carry their young longer before birth. The length of horse pregnancies from conception to birth varies according to a roughly Normal distribution with mean 336 days and standard deviation 3 days. Use the 68–95–99.7 rule to answer the following
Standard Normal distribution Use Table A (or technology) to find each of the following for a standard Normal distribution. In each case, sketch a standard Normal curve and shade the area of interest.(a) The proportion of observations with −2.25 < z < 1.77(b) The number z such that 35% of all
Low-birth-weight babies Researchers in Norway analyzed data on the birth weights of 400,000 newborns over a 6-year period. The distribution of birth weights is Normal with a mean of 3668 grams and a standard deviation of 511 grams.16 Babies that weigh less than 2500 grams at birth are classified as
Ketchup A fast-food restaurant has just installed a new automatic ketchup dispenser for use in preparing its burgers. The amount of ketchup dispensed by the machine follows a Normal distribution with mean 1.05 ounces and standard deviation 0.08 ounce.(a) If the restaurant’s goal is to put between
Grading managers Many companies “grade on a bell curve” to compare the performance of their managers and professional workers. This forces the use of some low performance ratings, so that not all workers are listed as “above average.” Ford Motor Company’s“performance management
Fruit fly thorax lengths Here are the lengths in millimeters of the thorax for 49 male fruit flies:17 0.64 0.64 0.64 0.68 0.68 0.68 0.72 0.72 0.72 0.72 0.74 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.78 0.80 0.80 0.80 0.80 0.80 0.82 0.82 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.88 0.88
Assessing Normality A Normal probability plot of a set of data is shown here. Would you say that these measurements are approximately Normally distributed?Why or why not? Expected z-score -1 -2- -3- 0 1- 3 2- Data values
Many professional schools require applicants to take a standardized test. Suppose that 1000 students take such a test. Several weeks after the test, Pete receives his score report: he got a 63, which placed him at the 73rd percentile. This means that(a) Pete’s score was below the median.(b) Pete
For the Normal distribution shown, the standard deviation is closest to -8 -6 -4 -2 0 2 4 6 00 8 10 12 (a) 0 (b) 1 (c) 2 (d) 3 (e) 5
Rainwater was collected in water collectors at 30 different sites near an industrial complex, and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60 and 1.10, respectively. When the pH meter was recalibrated back at the laboratory, it was found to
The figure shows a cumulative relative frequency graph of the number of ounces of alcohol consumed per week in a sample of 150 adults who report drinking alcohol occasionally. About what percent of these adults consume between 4 and 8 ounces per week?(a) 20% (b) 40% (c) 50% (d) 60% (e) 80% 88 100
The average yearly snowfall in Chillyville is Normally distributed with a mean of 55 inches. If the snowfall in Chillyville exceeds 60 inches in 15% of the years, what is the standard deviation?(a) 4.83 inches (d) 8.93 inches(b) 5.18 inches (e) The standard deviation cannot be computed from(c) 6.04
The figure shown is the density curve of a distribution.Seven values are marked on the density curve. Which of the following statements is true?(a) The mean of the distribution is E.(b) The area between B and F is 0.50.(c) The median of the distribution is C.(d) The 3rd quartile of the distribution
If the heights of a population of men follow a Normal distribution, and 99.7% have heights between 5′0″and 7′0″, what is your estimate of the standard deviation of the heights in this population?(a) 1″ (b) 3″ (c) 4″ (d) 6″ (e) 12″
Which of the following is not correct about a standard Normal distribution?(a) The proportion of scores that satisfy 0 < z < 1.5 is 0.4332.(b) The proportion of scores that satisfy z < −1.0 is 0.1587.(c) The proportion of scores that satisfy z > 2.0 is 0.0228.(d) The proportion of scores that
What is the standardized score (z-score) for a student who scored 500 on the old SAT scale?(a) −30 (b) −0.27 (c) −0.13 (d) 0.13 (e) 0.27
Gina took the SAT in 1994 and scored 500. Her cousin Colleen took the SAT in 2013 and scored 530. Who did better on the exam, and how can you tell?(a) Colleen—she scored 30 points higher than Gina.(b) Colleen—her standardized score is higher than Gina’s.(c) Gina—her standardized score is
As part of the President’s Challenge, students can attempt to earn the Presidential Physical Fitness Award or the National Physical Fitness Award by meeting qualifying standards in five events: curl-ups, shuttle run, sit and reach, one-mile run, and pullups.The qualifying standards are based on
The army reports that the distribution of head circumference among male soldiers is approximately Normal with mean 22.8 inches and standard deviation 1.1 inches.(a) A male soldier whose head circumference is 23.9 inches would be at what percentile? Show your method clearly.(b) The army’s helmet
A study recorded the amount of oil recovered from the 64 wells in an oil field. Here are descriptive statistics for that set of data from Minitab.Descriptive Statistics: Oilprod Variable n Mean Median StDev Min Max Q1 Q3 Oilprod 64 48.25 37.80 40.24 2.00 204.90 21.40 60.75 Does the amount of oil
Identify the population and sample in a statistical study.
Identify voluntary response samples and convenience samples.Explain how these sampling methods can lead to bias.
Describe how to obtain a random sample using slips of paper, technology, or a table of random digits.
Distinguish a simple random sample from a stratified random sample or cluster sample. Give the advantages and disadvantages of each sampling method.
Explain how undercoverage, nonresponse, question wording, and other aspects of a sample survey can lead to bias.
How Does the Current Population Survey Work?
A farmer brings a juice company several crates of oranges each week. A company inspector looks at 10 oranges from the top of each crate before deciding whether to buy all the oranges.
The ABC program Nightline once asked whether the United Nations should continue to have its headquarters in the United States. Viewers were invited to call one telephone number to respond “Yes” and another for “No.” There was a charge for calling either number. More than 186,000 callers
Students as customers A high school’s student newspaper plans to survey local businesses about the importance of students as customers. From an alphabetical list of all local businesses, the newspaper staff chooses 150 businesses at random. Of these, 73 return the questionnaire mailed by the
Student archaeologists An archaeological dig turns up large numbers of pottery shards, broken stone tools, and other artifacts. Students working on the project classify each artifact and assign it a number.The counts in different categories are important for understanding the site, so the project
Sampling stuffed envelopes A large retailer prepares its customers’ monthly credit card bills using an automatic machine that folds the bills, stuffs them into envelopes, and seals the envelopes for mailing. Are the envelopes completely sealed? Inspectors choose 40 envelopes at random from the
Customer satisfaction A department store mails a customer satisfaction survey to people who make credit card purchases at the store. This month, 45,000 people made credit card purchases. Surveys are mailed to 1000 of these people, chosen at random, and 137 people return the survey form. Identify
Call the shots An advertisement for an upcoming TV show asked: “Should handgun control be tougher?You call the shots in a special call-in poll tonight. If yes, call 1-900-720-6181. If no, call 1-900-720-6182.Charge is 50 cents for the first minute.” Over 90%of people who called in said
Explain it to the congresswoman You are on the staff of a member of Congress who is considering a bill that would provide government-sponsored insurance for nursing-home care. You report that 1128 letters have been received on the issue, of which 871 oppose the legislation. “I’m surprised that
Instant opinion A recent online poll posed the question “Should female athletes be paid the same as men for the work they do?’’ In all, 13,147(44%) said “Yes,’’ 15,182 (50%) said “No,’’ and the remaining 1448 said “Don’t know.” In spite of the large sample size for this
Sampling at the mall You have probably seen the mall interviewer, approaching people passing by with clipboard in hand. Explain why even a large sample of mall shoppers would not provide a trustworthy estimate of the current unemployment rate.
Sleepless nights How much sleep do high school students get on a typical school night? An interested student designed a survey to find out. To make data collection easier, the student surveyed the first 100 students to arrive at school on a particular morning.These students reported an average of
Online polls In June 2008, Parade magazine posed the following question: “Should drivers be banned from using all cell phones?” Readers were encouraged to vote online at parade.com. The July 13, 2008, issue of Parade reported the results: 2407(85%) said “Yes” and 410 (15%) said “No.”(a)
Do you trust the Internet? You want to ask a sample of high school students the question “How much do you trust information about health that you find on the Internet—a great deal, somewhat, not much, or not at all?” You try out this and other questions on a pilot group of 5 students chosen
Apartment living You are planning a report on apartment living in a college town. You decide to select three apartment complexes at random for indepth interviews with residents.(a) Explain how you would use a line of Table D to choose an SRS of 3 complexes from the list below.Explain your method
Sampling the forest To gather data on a 1200-acre pine forest in Louisiana, the U.S. Forest Service laid a grid of 1410 equally spaced circular plots over a map of the forest. A ground survey visited a sample of 10%of these plots.13(a) Explain how you would use your calculator or Table D to choose
Sampling gravestones The local genealogical society in Coles County, Illinois, has compiled records on all 55,914 gravestones in cemeteries in the county for the years 1825 to 1985. Historians plan to use these records to learn about African Americans in Coles County’s history.They first choose
Random digits Which of the following statements are true of a table of random digits, and which are false? Briefly explain your answers.(a) There are exactly four 0s in each row of 40 digits.(b) Each pair of digits has chance 1/100 of being 00.(c) The digits 0000 can never appear as a group,
Random digits In using Table D repeatedly to choose random samples, you should not always begin at the same place, such as line 101. Why not?
iPhones Suppose 1000 iPhones are produced at a factory today. Management would like to ensure that the phones’ display screens meet their quality standards before shipping them to retail stores. Since it takes about 10 minutes to inspect an individual phone’s display screen, managers decide to
Dead trees On the west side of Rocky Mountain National Park, many mature pine trees are dying due to infestation by pine beetles. Scientists would like to use sampling to estimate the proportion of all pine trees in the area that have been infected.(a) Explain why it wouldn’t be practical for
Who goes to the convention? A club has 30 student members and 10 faculty members. The students are Abel Fisher Huber Miranda Reinmann Carson Ghosh Jimenez Moskowitz Santos Chen Griswold Jones Neyman Shaw David Hein Kim O’Brien Thompson Deming Hernandez Klotz Pearl Utts Elashoff Holland Liu Potter
Sampling by accountants Accountants often use stratified samples during audits to verify a company’s records of such things as accounts receivable. The stratification is based on the dollar amount of the item and often includes 100% sampling of the largest items. One company reports 5000 accounts
Go Blue! Michigan Stadium, also known as “The Big House,” seats over 100,000 fans for a football game. The University of Michigan athletic department plans to conduct a survey about concessions that are sold during games. Tickets are most expensive for seats on the sidelines. The cheapest seats
How was your stay? A hotel has 30 floors with 40 rooms per floor. The rooms on one side of the hotel face the water, while rooms on the other side face a golf course. There is an extra charge for the rooms with a water view. The hotel manager wants to survey 120 guests who stayed at the hotel
Is it an SRS? A corporation employs 2000 male and 500 female engineers. A stratified random sample of 200 male and 50 female engineers gives each engineer 1 chance in 10 to be chosen. This sample design gives every individual in the population the same chance to be chosen for the sample. Is it an
Attitudes toward alcohol At a party there are 30 students over age 21 and 20 students under age 21. You choose at random 3 of those over 21 and separately choose at random 2 of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to
High-speed Internet Laying fiber-optic cable is expensive.Cable companies want to make sure that if they extend their lines out to less dense suburban or rural areas, there will be sufficient demand and the work will be cost-effective. They decide to conduct a survey to determine the proportion of
Tweet, tweet! What proportion of students at your school use Twitter? To find out, you survey a simple random sample of students from the school roster.(a) Will your sample result be exactly the same as the true population proportion? Explain.(b) Which would be more likely to get your sample result
Far from home? A researcher wants to estimate the average distance that students at a large community college live from campus. To find out, she surveys a simple random sample of students from the registrar’s database.(a) Will the researcher’s sample result be exactly the same as the true
Baseball tickets Suppose you want to know the average amount of money spent by the fans attending opening day for the Cleveland Indians baseball season. You get permission from the team’s management to conduct a survey at the stadium, but they will not allow you to bother the fans in the club
Rise and shine How long before school starts do students get out of bed, on average? Administrators survey a random sample of students on each school bus one morning.Give a reason why this survey might yield a biased result. Explain the likely direction of the bias.
Nonresponse A survey of drivers began by randomly sampling all listed residential telephone numbers in the United States. Of 45,956 calls to these numbers, 5029 were completed. The goal of the survey was to estimate how far people drive, on average, per day.15(a) What was the rate of nonresponse
Ring-no-answer A common form of nonresponse in telephone surveys is “ring-no-answer.” That is, a call is made to an active number but no one answers.The Italian National Statistical Institute looked at nonresponse to a government survey of households in Italy during the periods January 1 to
Running red lights The sample described in Exercise 31 produced a list of 5024 licensed drivers.The investigators then chose an SRS of 880 of these drivers to answer questions about their driving habits.One question asked was: “Recalling the last ten traffic lights you drove through, how many of
Seat belt use A study in El Paso, Texas, looked at seat belt use by drivers. Drivers were observed at randomly chosen convenience stores. After they left their cars, they were invited to answer questions that included questions about seat belt use. In all, 75% said they always used seat belts, yet

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