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Business Statistics

David F. Groebner, Patrick W. Shannon, Phillip C. Fry, Kent D. Smith

Chapter 3

Describing Data Using Numerical Measures - all with Video Answers

Educators


Chapter Questions

05:31

Problem 1

A random sample of 15 articles in a Fortune revealed the following word counts per article:
Compute the mean, median, first quartile, and third quartile for these sample data.

Pammi Eswari
Pammi Eswari
Numerade Educator
01:14

Problem 2

The following data reflect the number of defects produced on an assembly line at the Dearfield Electronics Company for the past 8 days.
a. Compute the mean number of defects for this population of days.
b. Compute the median number of defects produced for this population of days.
c. Determine if there is a mode number of defects and, if so, indicate the mode value.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:32

Problem 3

A European cereal maker recently sampled 20 of its medium-size oat cereal packages to determine the weights of the cereal in each package. These sample data, measured in ounces, are as follows:
Calculate the first and third quartiles for these sample data.

Carson Merrill
Carson Merrill
Numerade Educator
05:16

Problem 4

The time (in seconds) that it took for each of 16 vehicles to exit a parking lot in downtown Cincinnati is
Compute the mean, median, first quartile, and third quartile for the sample data.

JC
Jack Carlson
Numerade Educator
03:15

Problem 5

A random sample of the miles driven by 20 rental car customers is shown as follows:
Develop a box and whisker plot for the sample data.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:03

Problem 6

Examine the following data:
a. Compute the quartiles.
b. Calculate the 90th percentile.
c. Develop a box and whisker plot.
d. Calculate the 20th and the 30 th percentiles.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
00:49

Problem 7

Consider the following data that represent the commute distances for students who attend Emory University:
a. Determine the 80 th percentile.
b. Determine numbers that are the 25 th and 75 th percentiles.
c. Determine a number that qualifies as a median for these data.

Joseph Liao
Joseph Liao
Numerade Educator
13:57

Problem 8

A professor wishes to develop a numerical method for giving grades. He intends to base the grade on homework, two midterms, a project, and a final examination. He wishes the final exam to have the largest influence on the grade. He wants the project to have $10 \%$, each midterm to have $20 \%$, and the homework to have $10 \%$ of the influence of the semester grade.
a. Determine the weights the professor should use to produce a weighted average for grading purposes.
b. For a student with the following grades during the quarter, calculate a weighted average for the course:
c. Calculate an (unweighted) average of these five scores and discuss why the weighted average would be preferable here.

Michael Nartey
Michael Nartey
Numerade Educator
01:13

Problem 9

The manager for the Jiffy Lube in Saratoga, Florida, has collected data on the number of customers who agreed to purchase an air filter when they were also having their oil changed. The sample data are shown as follows:
a. Compute the mean, median, and mode for these data.
b. Indicate whether the data are skewed or symmetrical.
c. Construct a box and whisker plot for these data. Referring to your answer in part b, does the box plot support your conclusion about skewness? Discuss.

Jerelyn Nevil
Jerelyn Nevil
Numerade Educator
01:11

Problem 10

During the past few years, there has been a lot of discussion about the price of university textbooks. The complaints have come from many places, including students, faculty, parents, and even government officials. The publishing companies have been called on to explain why textbooks cost so much. Recently, one of the major publishing companies was asked to testify before a congressional panel in Washington, D.C. As part of the presentation, the president of the company organized his talk around four main areas: production costs, author royalties, marketing costs, and bookstore markup. He used one of his company's business statistics texts as an example when he pointed out the production costs-including editing, proofing, printing, bünding, inventory holding, and distributioncome to about $$\$32$$ per book sold. Authors receive $$\$12$$ per copy for the hundreds of hours of creative work in writing the book and supplementary materials. Marketing costs are pegged at about $$\$5$$ per copy sold and go to pay for the book sales force and examination copies sent to professors. The book is then sold to bookstores for $$\$ 70$$ per copy, a markup on costs of about $40 \%$ to cover overhead and the publishing costs associated with many upper-division, low-market texts that lose money for the company. Once university bookstores purchase the book, they mark it up. place it on the shelf, and sell it to the student. If books go unsold, they are returned to the publisher for a full refund. The following data reflect the dollar markup on the business statistics text for a sample of 20 college bookstores:
a. Compute the mean markup on the business statistics text by university bookstores in the sample.
b. Compute the median markup.
c. Determine the mode markup.
d. Write a short paragraph discussing the statistics computed in parts a-c.

Abdullah Alomair
Abdullah Alomair
Numerade Educator
03:20

Problem 11

The Xang Corporation operates five clothing suppliers in China to provide merchandise for Nike. Nike recently sought information from the five plants. One variable for which data were collected was the total money (in U.S. dollars) the company spent on medical support for its employees in the first three months of the year. Data on number of employees at the plants are also shown. These data are as follows:
a. Compute the weighted mean medical payments for these five plants using number of employees as the weights.
b. Explain why Nike would desire that a weighted average be computed in this situation rather than a simple numeric average.

James Kiss
James Kiss
Numerade Educator
00:46

Problem 12

The Tru-Green Lawn Company prowides yard care services for customers throughout the Denver area. The company owner recently tracked the time his field employees spent at a sample of customer locations. He was hoping to use these data to help him with his scheduling and to establish billing rates. The following sample data, in minutes, were recorded:
Describe the central tendency of these data by computing the mean, median, and mode. Based on these measures, can you conclude that the distribution of time spent at customer locations is skewed or symmetric?

Emily Himsel
Emily Himsel
Numerade Educator

Problem 13

Eastern States Bank and Trust monitors its drive-thru service times electronically to ensure that its speed of service is meeting the company's goals. A sample of 28 drive-thru times was recently taken and is shown here.
a. Compute the mean, median, and mode for these sample data.
b. Indicate whether the data are symmetrical or skewed.
c. Construct a box and whisker plot for the sample data. Does the box and whisker plot support your conclusions in part $b$ concerning the symmetry or skewness of these data?

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04:46

Problem 14

Todd Lindsey \& Associates, a commercial real estate company located in Boston, owns six office buildings in the Boston area that it leases to businesses. The lease price per square foot differs by building due to location and building amenities. Currently, all six buildings are fully leased at the prices shown here.
a. Compute the weighted average (mean) price per square foot for these buildings.
b. Why is the weighted average price per square foot preferred to a simple average price per square foot in this case?

Emily Burns
Emily Burns
Numerade Educator
07:01

Problem 15

Business Week recently reported that L. G. Philips LCD Co. would complete a new factory in Paju, South Korea. It will be the world's largest maker of liquidcrystal display panels. The arrival of the plant means that flat-panel LCD televisions would become increasingly affordable. The average retail cost of a $20^{\prime \prime}$ LCD television in 2000 was $$\$ 5,139$$. To obtain what the average retail cost of a $37^{\prime \prime}$ LCD was in 2008, a survey yielded the following data (in SU.S.):
a. Calculate the mean cost for these data.
b. Examine the data presented. Choose an appropriate measure of the center of the data, justify the choice, and calculate the measure.
c. The influence an observation has on a statistic may be calculated by deleting the observation and calculating the difference between the original statistic and the statistic with the data point removed. The larger the difference, the more influential the data point. Identify the data points that have the most and the least influence in the calculation of the sample mean.

Samuel Goyette
Samuel Goyette
Numerade Educator
04:27

Problem 16

Wageweb.com exhibits salary data obtained from surveys. It provides compensation information on over 170 benchmark positions, including finance positions. It reports the salaries of chief finance officers for midsined firms. Suppose that a sample is taken of the annual salaries for 25 CFO s. Assume the data are in thousands of dollars.
a. Calculate the mean salary of the CFOs.
b. Based on measures of the center of the data, determine if the CFO salary data are skewed.
c. Construct a box and whisker plot and summarize the characteristics of the CFO salaries that it reveals.

Jon Southam
Jon Southam
Numerade Educator

Problem 17

The Federal Deposit Insurance Corporation (FDIC) insures deposits in banks and thrift institutions for up to $$\$ 250,000$$. Before the banking crisis of late 2008 , there were $8,885 \mathrm{FDIC}$-insured institutions, with deposits of $$\$ 6,826,804,000,000$$. Bank of America had deposits of $\$ 681,570,000,000$ in nearly 6,000 banking centers during 2004 .
a. Calculate the average deposits per bank for both FDIC-insured institutions and Bank of America.
b. Deseribe the relationship between the two averages calculated in part a. Provide a reason for the disparity.
c. Would the two averages be considered to be parameters or statistics? Explain.

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Problem 18

Each year, Business Week publishes information and rankings of master of business administration (MBA) programs. The data file MBA Analysis contains data on several variables for eight reputable MBA programs as presented in the October 2, 2000, issue of Business Week. The variables include pre- and post-MBA salary, percentage salary increase, undergraduate GPA, average Graduate Management Admission Test (GMAT) score, annual tuition, and expected annual student cost. Compute the mean and median for each of the variables in the database and write a short report that summarizes the data. Include any appropriate charts or graphs to assist in your report.

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Problem 19

Dynamic random-access memory (DRAM) memory chips are made from silicon wafers in manufacturing facilities through a very complex process called wafer fabs. The wafers are routed through the fab machines in an order that is referred to as a recipe. The wafers may go through the same machine several times as the chip is created. The data file DRAM Chips contains a sample of processing times, measured in fractions of hours, at a particular machine center for one chip recipe.
a. Compute the mean processing time.
b. Compute the median processing time.
c. Determine what the mode processing time is.
d. Calculate the 80th percentile for processing time.

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01:29

Problem 20

Japolli Bakery tracks sales of its different bread products on a daily basis. The data for 22 consecutive days at one of its retail outlets in Nashville are in a file called Japolli Bakery. Calculate the mean, mode, and median sales for each of the bread categories and write a short report that describes these data. Use any charts or graphs that may be helpful in more fully describing the data.

Jingtian Li
Jingtian Li
Numerade Educator
02:28

Problem 21

Before the sub-prime loan crisis and the end of the "housing bubble" in 2008 the value of houses was escalating rapidly, as much as $40 \%$ a year in some areas. In an effort to track housing prices the National Association of Realtors developed the Pending Home Sales Index (PHSI), a new leading indicator for the housing market. An index of 100 is equal to the average level of contract activity during 2001, the first year to be analyzed. The index is based on a large national sample representing about $20 \%$ of home sales. The file entitled Pending contains the PHSI from January 2004 to August 2005.
a. Determine the mean and median for the PHSI between January 2004 and August 2005. Specify the shape of the PHSI's distribution.
b. The PHSI was at 111.0 in January 2004 and it was at 129.5 in August of 2005 . Determine the average monthly increase in the PHSI for this period.
c. Using your answer to part b, suggest a weighting scheme to calculate the weighted mean for the months between January 2004 and August 2005. Use the scheme to produce the weighted average of the PHSI in this time period.
d. Does the weighted average seem more appropriate here? Explain.

Zach Steedman
Zach Steedman
Numerade Educator
00:22

Problem 22

Homeowners and businesses pay taxes on the assessed value of their property. As a result, property taxes can be a problem for elderly homeowners who are on a fixed retirement income. Whereas these retirement incomes remain basically constant, because of rising real estate prices the property taxes in many areas of the country have risen dramatically. In some cases. homeowners are required to sell their homes because they can't afford the taxes. In Phoenix, Arizona, government officials are considering giving certain elderly homeowners a property tax reduction based on income. One proposal calls for all homeowners over the age of 65 with incomes at or below the 20th percentile to get a reduction in property taxes. A random sample of 50 people over the age of 65 was selected, and the household income (as reported on the most current federal tax return) was recorded. These data are also in the file called Property Tax Incomes. Use these data to establish the income cutoff point to qualify for the property tax cut.

Nick Johnson
Nick Johnson
Numerade Educator
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Problem 23

Suppose a random sample of 137 households in Detroit was taken as part of a study on annual houschold spending for food at home. The sample data are contained in the file Detroit Eats.
a. For the sample data, compute the mean and the median and construct a box and whisker plot.
b. Are the data skewed or symmetric?
c. Approximately what percent of the data values are between $$\$ 2,900$$ and $$\$ 3,250$$ ?

Jason Gerber
Jason Gerber
Numerade Educator
03:51

Problem 24

USA Todary reported a survey made by Nationwide Mutual Insurance that indicated the average amount of time spent to resolve identity theft cases was 81 hours. The file entitled Theft contains data that would produce this statistic.
a. Construct a stem and leaf display. Indicate the shape of data displayed by the stem and leaf display.
b. Use measures that indicate the shape of the distribution. Do these measures give results that agree with the shape shown in part a?
c. Considering your answers to part a and b, indicate which measure you would recommend using to indicate the center of the data.

James Kiss
James Kiss
Numerade Educator
02:29

Problem 25

Google is noted for its generous employee benefits. The following data reflect the number of vacation days that a sample of employees at Google have left to take before the end of the year:
a. Compute the range for these sample data.
b. Compute the variance for these sample data.
c. Compute the standard deviation for these sample data.

Brandon Cleary
Brandon Cleary
Numerade Educator
05:47

Problem 26

The following data reflect the number of times a population of business executives flew on business during the previous month:

$$
\begin{array}{llllll}
4 & 6 & 9 & 4 & 5 & 7
\end{array}
$$

a. Compute the range for these data.
b. Compute the variance and standard deviation.
c. Assuming that these data represent a sample rather than a population, compute the variance and standard deviation. Discuss the difference between the values computed here and in part b.

Trent Speier
Trent Speier
Numerade Educator
00:55

Problem 27

The following data are the population of ages of students who have recently purchased a sports video game:
a. Compute the population variance.
b. Compute the population standard deviation.

Deborah Ferry
Deborah Ferry
Numerade Educator
06:56

Problem 28

A county library in Minnesota reported the following number of books checked out in 15 randomly selected months:
Determine the range, variance, and standard deviation for the sample data.

Samuel Goyette
Samuel Goyette
Numerade Educator
View

Problem 29

The following data show the number of hours spent watching television for 12 randomly selected freshmen attending a liberal arts college in the Midwest:
Calculate the range, variance, standard deviation, and interquartile range for the sample data.

Shu Naito
Shu Naito
Numerade Educator
View

Problem 30

Consider the following two separate samples:
a. Calculate the range, variance, standard deviation, and interquartile range for each data set.
b. Which data set is most spread out based on these statistics?
c. Now remove the largest number from each data set and repeat the calculations called for in part a.
d. Compare the results of parts a and c. Which statistic seems to be most affected by outliers?

Susan Hallstrom
Susan Hallstrom
Numerade Educator
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Problem 31

The following set of data shows the number of alcoholic drinks that students at a Kansas university reported they had consumed in the past month:
a. Assume the data set is a sample. Calculate the range, variance, standard deviation, and interquartile range for the data set.
b. Assume the data set is a population. Calculate the range, variance, standard deviation, and interquartile range for the data set.
c. Indicate the relationship between the statistics and the respective parameters calculated in parts a and $\mathbf{b}$.

Shu Naito
Shu Naito
Numerade Educator
00:23

Problem 32

Easy Connect, Inc., provides access to computers for business uses. The manager monitors computer use to make sure that the number of computers is sufficient to meet the needs of the customers. Recently, the manager collected data on a sample of customers and tracked the time the customers started working at a computer until they were finished. The elapsed times, in minutes, are shown as follows:
Compute appropriate measures of the center and variation to describe the time customers spend on the computer.

Kimberly Waterbury
Kimberly Waterbury
Numerade Educator
18:39

Problem 33

A random sample of 20 pledges to a public radio fundraiser revealed the following dollar pledges:
a. Compute the range, variance, standard deviation, and interquartile range for these sample data.
b. Briefly explain the difference between the range and the interquartile range as a measure of dispersion.

Paul A.
Paul A.
California State Polytechnic University, Pomona
00:54

Problem 34

Gold's Gym selected a random sample of 10 customers and monitored the number of times each eustomer used the workout facility in a one-month period. The following data were collected:
$$
\begin{array}{llllllllll}
10 & 19 & 17 & 19 & 12 & 20 & 20 & 15 & 16 & 13
\end{array}
$$
Gold's managers are considering a promotion in which they reward frequent users with a small gift. They have decided that they will only give gifts to those customers whose number of visits in a one-month period is 1 standard deviation above the mean. Find the minimum number of visits required to receive a gift.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
05:38

Problem 35

The registrar at Whitworth College has been asked to prepare a report about the graduate students. Among other things, she wants to analyze the ages of the students. She has taken a sample of 10 graduate students and has found the following ages:
$\begin{array}{llllllllll}32 & 22 & 24 & 27 & 27 & 33 & 28 & 23 & 24 & 21\end{array}$
a. Compute the range, interquartile range, and the standard deviation for these data.
b. An earlier study showed that the mean age of graduate students in U.S. colleges and universities is 37.8 years. Based on your calculations in part a, what might you conclude about the age of students in Whitworth's programs?

Samuel Goyette
Samuel Goyette
Numerade Educator
03:37

Problem 36

The branch manager for the D. L. Evens Bank has been asked to prepare a presentation for next week's board meeting. At the presentation, she will discuss the status of her branch's loans issued for recreation vehicles (RVs). In particular, she will analyze the loan balances for a sample of 10 RV loans. The following data were collected:
a. Compute the mean loan balance.
b. Compute the loan balance standard deviation.
c. Write a one-paragraph statement that uses the statistics computed in parts $a$ and $b$ to describe the RV loan data at the branch.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
04:21

Problem 37

A parking garage in Memphis monitors the time it takes customers to exit the parking structure from the time they get in their car until they are on the streets. A sample of 28 exits was recently taken and is shown here.
a. Calculate the range, interquartile range, variance, and standard deviation for these sample data.
b. If the minimum time and the maximum time in the sample data are both increased by 10 seconds, would this affect the value for the interquartile range that you calculated in part a? Why or why not?
c. Suppose the clock that electronically recorded the times was not working properly when the sample was taken and each of the sampled times needs to be increased by 10 seconds. How would adding 10 seconds to each of the sampled speed of service times change the sample variance of the data?

Maxime Rossetti
Maxime Rossetti
Numerade Educator
01:13

Problem 38

Nielsen Monitor-Plus, a service of Nielsen Media Research, is one of the leaders in advertising information services in the United States, providing advertising activity for 16 media, including television tracking, in all 210 Designated Market Areas (DMAs). One of the issues it has researched is the increasing amount of "clutter"-nouprogramming minutes in an hour of prime time-including network and local commercials and advertisements for other shows. Recently it found the average nonprogramming minutes in an hour of prime-time broadcasting for network television was $15: 48$ minutes. For cable television, the average was $14: 55$ minutes.
a. Calculate the difference in the average clutter between network and cable television.
b. Suppose the standard deviation in the amount of clutter for both the network and cable television was either 5 minutes or 15 seconds. Which standard deviation would lead you to conclude that there was a major difference in the two clutter averages? Comment.

Dominador Tan
Dominador Tan
Numerade Educator
03:07

Problem 39

The Bureau of Labor Statistics in its Monthly Labor Review published the "over-the-month" percent change in the price index for imports from April 2004 to April 2005. These data are reproduced next.
a. Calculate the mean, standard deviation, and the interquartile range for the nine months of 2004 and the four months of 2005.
b. Compare the two averages that were calculated in part a. What do these two measurements indicate about the price index in each time period?
c. Compare the two standard deviations that were calculated in part a. What do these two measurements indicate about the price index in each time period?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:11

Problem 40

The U.S. Government Accountability Office recently indicated the price of college textbooks has been rising an average of $6 \%$ annually since the academic year 1987-1988. The report estimated that the average cost of books and supplies for first-time, full-time students at fout-year public universities for the academic year had reached $$\$ 898$$. A data set that would produce this average follows:
a. Calculate the mean and standard deviation.
b. Determine the number of standard deviations the most extreme cost is away from the mean. If you were to advise a prospective stadent conceming the moncy the student should save to afford the cost of books and supplies for at least $90 \%$ of the colleges, determine the amount you would suggest.

Abdullah Alomair
Abdullah Alomair
Numerade Educator
01:15

Problem 41

The manager of a phone kiosk in the Valley Mall recently collected data on a sample of 50 customers who purchased a cell phone and a monthly call plan. The data she recorded are in the data file called Phone Survey.
a. The manager is interested in describing the difference between male and female customers with respect to the price of the phone purchased. She wants to compute mean and standard deviation of phone purchase price for each group of customers.
b. The manager is also interested in an analysis of the phone purchase price based on whether the use will be for home or business. Again, she wants to compute mean and standard deviation of phone purchase price for each group of customers.

Nick Johnson
Nick Johnson
Numerade Educator

Problem 42

Each year, Business Week publishes information and rankings of MBA programs. The data file MBA Analysis contains data on several variables for eight reputable MBA programs as presented in the October 2, 2000, issue of Business Week. The variables include pre- and post-MBA salary, percentage salary increase. undergraduate GPA, average GMAT score, annual tuition, and expected annual student cost. Compute the mean, median, range, variance, and the standard deviation for each of the variables in the database and write a short report that summarizes the data using these measures. Include any appropriate charts or graphs to assist in your report.

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02:28

Problem 43

The First City Real Estate Company lists and sells residential real estate property in and around Yuma, Arizona. At a recent company meeting, the managing partner asked the office administrator to provide a descriptive analysis of the asking prices of the homes the company currently has listed. This list includes 319 homes; the price data, along with other home characteristics, are included in the data file called First City Real Estate. These data constitute a population.
a. Compute the mean listing price.
b. Compute the median listing price.
c. Compute the range in listing prices.
d. Compute the standard deviation in listing prices.
e. Write a short report using the statistics computed in parts a-d to describe the prices of the homes currently listed by First City Real Estate.

Zach Steedman
Zach Steedman
Numerade Educator

Problem 44

Suppose an investigation to determine whether the increased availability of generic drugs, Internet drug purchases, and cost controls have reduced out-ofpocket drug expenses. As a part of the investigation, a random sample of 196 privately insured adults with incomes above $200 \%$ of the poverty level was taken. and their 2005 out-of-pocket medical expenses for prescription drugs were collected. The data are in the file Drug Expenses.
a. Calculate the mean and median for the sample data.
b. Calculate the range, variance, standard deviation, and interquartile range for the sample data.
c. Construct a box and whisker plot for the sample data.
d. Write a short report that describes out-of-pocket drug expenses for privately insured adults whose incomes are greater than $200 \%$ of the poverty level.

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04:08

Problem 45

Executive MBA programs have become increasingly popular. In an article entitled "The Best Executive MBAs," Business Week provided data concerning the top 25 executive MBA programs. The tuition for each of the schools selected was given. A file entitled EMBA contains this data.
a. Calculate the $20 \mathrm{th}, 40 \mathrm{th}, 60$ th, and 80 th percentile among the ranks.
b. Calculate the mean and standard deviation of the tuition for the five subgroups defined by the rank percentiles in part a. (Hin: For this purpose, are the data subgroups samples or populations?
c. Do the various subgroups' descriptive statistics echo their standing among the listed programs? Comment.

Foster Wisusik
Foster Wisusik
Numerade Educator
04:27

Problem 46

When PricewaterhouseCoopers Saratoga released its 2005/2006 Human Capital Index Report it indicated that the average hiring cost for an American company to fill a job vacancy in 2004 was $$\$ 3,270$$. Sample data for recent job hires is in a file entitled Hired.
a. Calculate the variance and standard deviation for the sample data.
b. Construct a box and whisker plot. Does this plot indicate that extreme values (outliers) may be inflating the measures of spread calculated in part a?
c. Suggest and calculate a measure of spread that is not affected by outliers.

Jon Southam
Jon Southam
Numerade Educator
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Problem 47

A population of unknown shape has a mean of 3,000 and a standard deviation of 200 .
a. Find the minimum proportion of observations in the population that are in the range 2,600 to 3,400 .
b. Determine the maximum proportion of the observations that are above 3,600 .
c. What statement could you make concerning the proportion of observations that are smaller than 2,400?

James Kiss
James Kiss
Numerade Educator
02:29

Problem 48

The mean time that a certain model of light bulb will last is 400 hours, with a standard deviation equal to 50 hours.
a. Calculate the standardized value for a light bulb that lasts 500 hours.
b. Assuming that the distribution of hours that light bulbs last is bell-shaped, what percentage of bulbs could be expected to last longer than 500 hours?

Christopher Stanley
Christopher Stanley
Numerade Educator
01:21

Problem 49

Consider the following set of sample data:
a. Compute the mean and standard deviation for these sample data.
b. Calculate the coefficient of variation for these sample data and interpret its meaning.
c. Using Tchebysheff's theorem, determine the range of values that should include at least $89 \%$ of the data. Count the number of data values that fall into this range and comment on whether your interval range was conservative or not.

Hailey Tomashek
Hailey Tomashek
Numerade Educator
01:33

Problem 50

You are given the following parameters for two populations:
a. Compute the coefficient of variation for each population.
b. Based on the answers to part $a$, which population has data values that are more variable relative to the size of the population mean?

Hailey Tomashek
Hailey Tomashek
Numerade Educator
02:30

Problem 51

Two distributions of data are being analyzed. Distribution A has a mean of 500 and a standard deviation equal to 100 . Distribution $B$ has a mean of 10 and a standard deviation equal to 4.0. Based on this information, use the coefficient of variation to determine which distribution has greater relative variation.

Natalie Anderson
Natalie Anderson
Numerade Educator
02:30

Problem 52

Given two distributions with the following characteristics:
If a value from distribution $A$ is 50,000 and a value from distribution B is 40.0 , convert each value to a standardized $z$ value and indicate which one is relatively closer to its respective mean.

Natalie Anderson
Natalie Anderson
Numerade Educator
03:21

Problem 53

If a sample mean is 1,000 and the sample standard deviation is 250 , determine the standardized value for
a. $x=800$
b. $x=1,200$
c. $x=1,000$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
07:21

Problem 54

The following data represent random samples taken from two different populations, A and B :
a. Compute the mean and standard deviation for the sample data randomly selected from population A.
b. Compute the mean and standard deviation for the sample data randomly selected from population B.
c. Which sample has the greater spread when measured by the standard deviation?
d. Compute the coefficient of variation for the sample data selected from population A and from population B. Which sample exhibits the greater relative variation?

Vaidik Stats
Vaidik Stats
Numerade Educator
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Problem 55

Consider the following sample:
a. Calculate the mean and standard deviation for this data.
b. Determine the percentage of data values that fall in each of the following intervals: $\bar{x} \pm s, \bar{x} \pm 2 s$, $\bar{x} \pm 3$ s.
c. Compare these with the percentages that should be expected from a bell-shaped distribution. Does it seem plausible that these data came from a bellshaped population? Explain.

Victor Salazar
Victor Salazar
Numerade Educator
04:05

Problem 56

Consider the following population:
a. Determine the mean and variance.
b. Determine the percentage of data values that fall in each of the following intervals: $\bar{x} \pm 2 s, \bar{x} \pm 3 s$, $\bar{x} \pm 4 s$.
c. Compare these with the percentages specified by Tchebysheff's theorem.

Sophie Knight
Sophie Knight
Numerade Educator
02:34

Problem 57

Pfizer, Inc., a major U.S. pharmaceutical company, is developing a new drug aimed at reducing the pain associated with migraine headaches. Two drugs are currently under development. One consideration in the evaluation of the medication is how long the painkilling effects of the drugs last. A random sample of 12 tests for each drug revealed the following times (in minutes) until the effects of the drug were neutralized. The random samples are as follows:
a. Calculate the mean and standard deviation for each of the two drugs.
b. Based on the sample means calculated in part a, which drug appears to be effective longer?
c. Based on the sample standard deviations calculated in part a, which drug appears to have the greater variability in effect time?
d. Calculate the sample coefficient of variation for the two drugs. Based on the coefficient of variation, which drug has the greater variability in its time until the effect is neutralized?

Kari Hasz
Kari Hasz
Numerade Educator

Problem 58

Wells Fargo Bank's call center has representatives that speak both English and Spanish. A random sample of 11 calls to English-speaking service representatives and a random sample of 14 calls to Spanish-speaking service representatives was taken and the time to complete the calls was measured. The results (in seconds) are as follows:
a. Compute the mean and standard deviation for the time to complete calls to English-speaking service representatives.
b. Compute the mean and standard deviation for the time to complete calls to Spanish-speaking service representatives.
c. Compute the coefficient of variation for the time to complete calls to English-speaking and Spanishspeaking service representatives. Which group has the greater relative variability in the time to complete calls?
d. Construct box and whisker plots for the time required to complete the two types of calls and briefly discuss.

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03:58

Problem 59

Lockheed-Martin is a supplier for the aerospace industry. Recently, the company was considering switching to Cirus Systems, Inc., a new supplier for one of the component parts it needs for an assembly. At issue is the variability of the components supplied by Cirus Systems, Inc., compared to that of the existing supplier. The existing supplier makes the desired part with a mean diameter of 3.75 inches and a standard deviation of 0.078 inches. Unfortunately, Lockheed-Martin does not have any of the exact same parts from the new supplier. Instead, the new supplier has sent a sample of 20 parts of a different size that it claims are representative of the type of work it can do. These sample data are shown here and in the data file called Cirus.
Prepare a short letter to Lockheed-Martin indicating which supplier you would recommend based on relative variability.

Victor Salazar
Victor Salazar
Numerade Educator
01:17

Problem 60

A recent article in The Washington Post Weekly Edition indicated that about $80 \%$ of the estimated $$\$ 200$$ billion of federal housing subsidies consists of tax breaks (mainly deductions for mortgage interest payments and preferential treatment for profits on home sales). Federal housing benefits average $$\$ 8,268$$ for those with incomes between $$\$ 50,000$$ and $$\$ 200,000$$ and $$\$ 365$$ for those with income of $$\$ 40,000$$ to $$\$ 50,000$$. Suppose the standard deviations of the housing benefits in these two categories were equal to $$\$ 2,750$$ and $$\$ 120$$, respectively.
a. Examine the two standard deviations. What do these indicate about the range of benefits enjoyed by the two groups?
b. Repeat part a using the coefficient of variation as the measure of relative variation.

Lucas Finney
Lucas Finney
Numerade Educator
04:18

Problem 61

Anaheim Human Resources, Inc., performs employment screening for large companies in southern California. It usually follows a two-step process. First, potential applicants are given a test that cowers basic knowledge and intelligence. If applicants score between a certain range, they are called in for an interview. If they score below a certain point, they are sent a rejection letter. If applicants score above a certain point, they are sent direetly to the client's human resources office without the interview. Recently, Anaheim Human Resources began working with a new client and formulated a new test just for this company. Thirty people were given the test, which is supposed to produce scores that are distributed according to a bell-shaped distribution. The following data reflect the scores of those 30 people:
Anaheim Human Resources has in the past issued a rejection letter with no interview to the lower $16 \%$ taking the test. They also send the upper $2.5 \%$ directly to the company without an interview. Everyone else is interviewed. Based on the data and the assumption of a bell-shaped distribution, what score should be used for the two cutoffs?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
04:38

Problem 62

The College Board's Annual Survey of Colleges provides up-to-date information on tuition and other expenses associated with attending public and private nonprofit institutions of postsecondary education in the United States. Each fall, the College Board releases the survey results on how much colleges and universities are charging undergraduate students in the new academic year. The survey indicated that the average published tuition and fees for 2005-2006 were $$\$ 5,491$$ at public four-year colleges and universities and $$\$ 21.235$$ at private, nomprofit four-year colleges and universities. The standard deviation was approximately $$\$ 3,000$$ at public four-year colleges and universities and approximately $$\$ 10,000$$ for private colleges and universities.
a. Do the private, nomprofit four-year colleges and universities have the larger relative variability? Provide statistical evidence to support your answer.
b. If the data on published tuition and fees were bellshaped, determine the largest and smallest amount paid at the four-year private, nonprofit colleges and universities.
c. Based on your answer to part b, do you believe that the data are bell-shaped? Support your answer using statistical reasoning.

Robin Corrigan
Robin Corrigan
Numerade Educator
09:11

Problem 63

April 15 of every year is a day that most adults in the United States can relate to-the day that federal and state income taxes are duc. Although there have been several attempts by Congress and the Internal Revenue Service over the past few years to simplify the income tax process, many people still have a difficult time completing their tax returns properly. To draw attention to this problem, a West Coast newspaper has asked 50 certified public accountant (CPA) firms to complete the same tax return for a hypothetical head of houschold. The CPA firms have their tax experts complete the return with the objective of determining the total federal income tax liability. The data in the file called Taxes show the taxes owed as figured by each of the 50 CPA firms. Theoretically, they should all come up with the same taxes owed.

Based on these data, write a short article for the paper that describes the results of this experiment. Include in your article such descriptive statistics as the mean, median, and standard deviation. You might consider using percentiles, the coefficient of variation, and Tchebysheff's theorem to help describe the data.

Srikar Katta
Srikar Katta
Numerade Educator
03:57

Problem 64

Nike ONE Black is one of the golf balls Nike, Inc., produces. It must meet the specifications of the United States Golf Association (USGA). The USGA mandates that the diameter of the ball shall not be less than 1.682 inches ( 42.67 mm ). To verify that this specification is met, sample golf balls are taken from the production line and measured. These data are found in the file entitled Diameter.
a. Calculate the mean and standard deviation of this sample.
b. Examine the specification for the diameter of the golf ball again. Does it seem that the data could possibly be bell-shaped? Explain.
c. Determine the proportion of diameters in the following intervals: $\bar{x} \pm 2 s, \bar{x} \pm 3 s, \bar{x} \pm 4 s$. Compare these with the percentages specified by Tchebysheff's theorem.

Amany Waheeb
Amany Waheeb
Numerade Educator
02:11

Problem 65

The Centers for Disease Control and Prevention (CDC) started the Vessel Sanitation Program (VSP) in the early 1970s because of several disease outbreaks on cruise ships. The VSP was established to protect the health of passengers and crew by minimizing the risk of gastrointestinal illness on cruise ships. Inspections are scored on a point system of maximum 100, and cruise ships earn a score based on the criteria. Ships that score an 86 or higher have a satisfactory sanitation level. Data from a recent inspection are contained in a file entitled Cruiscore.
a. Calculate the mean, standard deviation, median. and interquartile range. Which of these measures would seem most appropriate to characterize this data set?
b. Produce a box and whisker plot of the data. Would the Empirical Rule or Tchebysheff's theorem be appropriate for describing this data set? Explain.
c. If you wished to travel only on those ships that are at the 90th percentile or above in terms of sanitation, what would be the lowest sanitation score you would find acceptable?

Nick Johnson
Nick Johnson
Numerade Educator
03:32

Problem 66

Airfare prices were collected for a round-trip from Los Angeles (LAX) to San Francisco (SFO). Airfare prices were also collected for a round-trip from Los Angeles (LAX) to Barcelona, Spain (BCN). Airfares were obtained for the designated and nearby airports. The passenger was to fly coach class round-trip, staying seven days. The data are contained in a file entitled Airfare.
a. Calculate the mean and standard deviation for each of the flights.
b. Calculate an appropriate measure of the relative variability of these two flights.
c. A British friend of yours is currently in Barcelona and wishes to fly to Los Angeles. If the flight fares are the same but priced in English pounds, determine his mean, standard deviation, and measure of relative dispersion for that data.

John Long
John Long
Numerade Educator
03:58

Problem 67

Doing business internationally is no longer something reserved for the largest companies. In fact, mediumsize and, in some cases, even small companies are finding themselves with the opportunity to do business internationally. One factor that will be important for world trade is the growth rate of the population of the world's countries. The data file called Countries contains data on the 2000 population and the growth rate between 1990 and 2000 for 74 countries throughout the world. Based on these data, which countries had growth rates that exceeded 2 standard deviations higher than the mean growth rate? Which countries had growth rates more than 2 standard deviations below the mean growth rate?

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator