## Question

2.7 The Transportation Security Administration reported that from January 1, 2008, to February 18, 2009, more than 14,000 banned items were collected at Palm Beach International Airport. The categories were as follows:

Category Frequency

Flammables/irritants 8,350

Knives and blades 4,134

Prohibited tools 753

Sharp objects 497

Other 357

a. Compute the percentage of values in each category.

b. What conclusions can you reach concerning the banned items?

2.17 The file contains the total cost ($) for four tickets, two beers, four soft drinks, four hot dogs, two game programs, two baseball caps, and parking for one vehicle at each of the 30 Major League Baseball parks during the 2010 season. These costs were

172,335,250,180,173,162,132,207,316,178,184,141,168,208,115

158,330,151,161,170,212,222,160,227,227,127,217,121,221,216

Source: Data extracted from teammarketing.com, April 1, 2010.

a. Organize these costs as an ordered array.

b. Construct a frequency distribution and a percentage distribution for these costs.

c. Around which class grouping, if any, are the costs of attending a baseball game concentrated? Explain.

2.19 One operation of a mill is to cut pieces of steel into parts that will later be used as the frame for front seats in an automobile. The steel is cut with a diamond saw and requires the resulting parts to be within inch of the length specified by the automobile company. Data are collected from a sample of 100 steel parts and stored in .The measurement reported is the difference in inches between the actual length of the steel part, as measured by a laser measurement device, and the specified length of the steel part. For example, the first value, represents a steel part that is 0.002 inch shorter than the specified length.

a. Construct a frequency distribution and a percentage distribution.

b. Construct a cumulative percentage distribution.

c. Is the steel mill doing a good job meeting the requirements set by the automobile company? Explain

2.21 The manufacturing company in Problem 2.20 also produces electric insulators. If the insulators break when in use, a short circuit is likely to occur. To test the strength of the insulators, destructive testing in high-powered labs is carried out to determine how much force is required to break the insulators. Force is measured by observing how many pounds must be applied to the insulator before it breaks. Force measurements are collected from a sample of 30 insulators and stored in Force and shown here:

1,870 1,728 1,656 1,610 1,634 1,784 1,522 1,696

1,592 1,662 1,866 1,764 1,734 1,662 1,734 1,774

1,550 1,756 1,762 1,866 1,820 1,744 1,788 1,688

1,810 1,752 1,680 1,810 1,652 1,736

a. Construct a frequency distribution and a percentage

distribution.

b. Construct a cumulative percentage distribution.

c. What can you conclude about the strength of the insulators if the company requires a force measurement of at least 1,500 pounds before the insulator breaks?

2.50 College basketball is big business, with coaches’ salaries, revenues, and expenses in millions of dollars. The file contains the coaches’ salary and revenue for college basketball at 60 of the 65 schools that played in the 2009 NCAA men’s basketball tournament (data extracted from “Compensation for Division 1 Men’s Basketball Coaches,” USA Today, April 2, 2010, p. 8C; and

C. Isadore, “Nothing but Net: Basketball Dollars by School,” money.cnn.com/2010/03/18/news/companies/basketball_profits/).

a. Do you think schools with higher revenues also have higher coaches’ salaries?

b. Construct a scatter plot with revenue on the X axis and coaches’ salaries on the Y axis.

c. Does the scatter plot confirm or contradict your answer to (a)?

2.51 College football players trying out for the NFL are given the Wonderlic standardized intelligence test. The file contains the average Wonderlic scores of football players trying out for the NFL and the graduation rate for football players at selected schools (data extracted from S. Walker, “The NFL’s Smartest Team,” The Wall Street Journal, September 30, 2005, pp. W1, W10).

a. Construct a scatter plot with average Wonderlic score on the X axis and graduation rate on the Y axis.

b. What conclusions can you reach about the relationship between the average Wonderlic score and graduation rate?

3.11 The file contains the cost (in cents) per 1-ounce serving for a sample of 13 chocolate chip cookies. The data are as follows:

54 22 25 23 36 43 7 43 25 47 24 45 44

Source: Data extracted from “Chip, Chip, Hooray,” Consumer Reports, June 2009, p. 7.

a. Compute the mean, median, and mode.

b. Compute the variance, standard deviation, range, coefficient of variation, and Z scores. Are there any outliers? Explain.

c. Are the data skewed? If so, how?

d. Based on the results of (a) through (c), what conclusions can you reach concerning the cost of chocolate chip cookies?

3.15 A bank branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1:00 P.M. lunch period. The waiting time, in minutes, is defined as the time the customer enters the line to when he or she reaches the teller window. Data are collected from a sample of 15 customers during this hour. The file contains the results, which are also listed here:

4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20

4.50 6.10 0.38 5.12 6.46 6.19 3.79

a. Compute the mean and median.

b. Compute the variance, standard deviation, range, coefficient of variation, and Z scores. Are there any outliers? Explain.

c. Are the data skewed? If so, how?

d. As a customer walks into the branch office during the lunch hour, she asks the branch manager how long she can expect to wait. The branch manager replies, “Almost certainly

less than five minutes.” On the basis of the results of (a) through (c), evaluate the accuracy of this statement.

3.21 The file contains the cost (in cents) per 1-ounce serving, for a sample of 13 chocolate chip

cookies. The data are as follows:

54 22 25 23 36 43 7 43 25 47 24 45 44

Source: Data extracted from “Chip, Chip, Hooray,” Consumer

Reports, June 2009, p. 7.

a. Compute the first quartile (Q1) the third quartile (Q3) and the interquartile range.

b. List the five-number summary.

c. Construct a boxplot and describe its shape.

3.40 The file lists the calories and sugar, in grams, in one serving of seven breakfast cereals:

Cereal Calories Sugar

Kellogg’s All Bran 80 6

Kellogg’s Corn Flakes 100 2

Wheaties 100 4

Nature’s Path Organic Multigrain 110 4

Flakes

Kellogg's Rice Krispies 130 4

Post Shredded Wheat Vanilla 190 11

Almond

Kellogg's Mini Wheats 200 10

a. Compute the covariance.

b. Compute the coefficient of correlation.

c. Which do you think is more valuable in expressing the relationship between calories and sugar—the covariance or the coefficient of correlation? Explain.

d. Based on (a) and (b), what conclusions can you reach about the relationship between calories and sugar?

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2.7 The Transportation Security Administration reported that from January 1, 2008, to February 18, 2009, more than 14,000 banned items were collected at Palm Beach International Airport. The categories were as follows:Category Frequency

Flammables/irritants 8,350

Knives and blades 4,134

Prohibited tools 753

Sharp objects 497

Other 357

a. Compute the percentage of values in each category.

Category Frequency Percentage

Flammables/irritants 8,350 59.26

Knives and blades 4,134 29.34

Prohibited tools 753 5.34

Sharp objects 497 3.53

Other 357 2.53

Total 14,091 100

b. What conclusions can you reach concerning the banned items?

The data indicated that flammables and irritants account for the highest proportion or most of banned items, followed by knives and blades with the proportion of 59.2 and 29.3 percent respectively. Other items contributed to the least proportion of banned items collected.

This implies that travelers prefer carrying flammables and irritants regularly although they are banned as compared to knives and blades, sharp objects and others....