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business
business statistics in practice

Questions and Answers of Business Statistics In Practice

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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 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
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”
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
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
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’
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)
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
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
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
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
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
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
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
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-
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
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
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
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)
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
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
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
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
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:
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
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
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”
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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

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