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Chapter 2: Q-81E (page 63)

Sanitation inspection of cruise ships. Refer to the Centres for Disease Control and Prevention listing of the October 2015 sanitation scores for 20 cruise ships, Exercise 2.24 (p. 83).

a. Find the mean and standard deviation of the sanitation scores.

b. Calculate the intervals x {s, x {2s, x {3s.

c. Find the percentage of measurements in the data set that fall within each interval, part

b. Do these percentages agree with Chebyshev鈥檚 Rule? The Empirical Rule?

Short Answer

Expert verified

a) Mean = 89.55

S = 4.71811

b) The interval for s (84.8319, 94.26811)

The interval for 2s (80.113, 98.986)

The interval for 3s (75.395, 103.7043)

c) s is 70%

2s is 95%

3s is 100%

b) Both are agreeable.

Step by step solution

01

(a) Mean and standard deviation

Mean=120脳96 + 93 +....+ 95 + 91X-=179120X-= 89.55S =1n-1鈭�i=1nx1-x炉2=119鈭�i=1nx1-2=4.71811

02

(b) or (c) Intervals calculate and percentage of measurement

X-卤S=84.8319,94.26811=1420脳100=70%X-卤2S=80.113,98.986Out of 20,19 numbers satisfied=1920脳100=95%X-卤3S=75.395,103.7043All numbers satisfied=100%

03

(b) Chebyshev’s

Chebyshev鈥檚 rule,

P1脳x-渭猢�K蟽猢�1K2P1脳x-渭猢�K蟽猢�1-1K2P1x-89.55猢�15猢�1-1P1x-89.55猢�15猢�0P1x-89.55猢�25猢�1-14P1x-89.55猢�25猢�0.75P1x-89.55猢�35猢�1-19P1x-89.55猢�35猢�0.889

Yes, it agrees with Chebyshev鈥檚 rule,

The empirical rule is,

x炉卤蟽is 68%x炉卤2蟽is 95%x炉卤3蟽is 99.7%

The empirical rule is also satisfied.

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Most popular questions from this chapter

Top credit card issuers, by region. The Nilson Report (December 2015) published a list of the top 150 credit card issuers worldwide. The issuers (e.g., American Express, MasterCard, Visa) were ranked based on outstanding debt during the year. The table gives a breakdown of the regions in the world served by the top 150 credit card issuers.

Worldwide Region

Number of credit
card issuers



Asia-Pacific

48


Canada

10


Europe

34


Latin America

29


Middle East/Africa

3


United States

26


Total

150


a. One of the top 150 credit card issuers is selected at random, and the region it serves is determined. What type of data (quantitative or qualitative) is measured?

b. For each region in the table, calculate the percentage of the 150 top credit card issuers that fall into that region.

c. Use the percentages, part b, to construct a relative frequency bar graph for the data summarized in the table.

d. Based on the bar graph, make a statement about the regions that most of the top 150 credit card users serve.

Performance of stock screeners.Investment companies provide their clients with automated tools鈥攃alled stock screeners鈥攖o help them select a portfolio of stocks to invest in. The American Association of Individual Investors (AAII) provides statistics on stock screeners at its Website, www.aaii.com. The next table lists the annualized percentage return on investment (as compared to the Standard & Poor鈥檚 500 Index) for 13 randomly selected stock screeners. (Note:A negative annualized return reflects a stock portfolio that performed worse than the S&P 500.)

(9.0, -.1, -1.6, 14.6, 16.0, 7.7, 19.9, 9.8, 3.2, 24.8, 17.6, 10.7, 9.1)

a.Compute the mean for the data set. Interpret its value.

b.Compute the median for the data set. Interpret its value.

Blue- vs. red-colored exam study. In a study of how external clues influence performance, university professors gave two different forms of a midterm examination to a large group of introductory students. The questions on the exam were identical and in the same order, but one exam was printed on blue paper and the other on red paper (Teaching Psychology, May 1998). Grading only the difficult questions on the exam, the researchers found that scores on the blue exam had a distribution with a mean of 53% and a standard deviation of 15%, while scores on the red exam had a distribution with a mean of 39% and a standard deviation of 12%. (Assume that both distributions are approximately mound-shaped and symmetric.)

a. Give an interpretation of the standard deviation for the students who took the blue exam.

b. Give an interpretation of the standard deviation for the students who took the red exam.

c. Suppose a student is selected at random from the group of students who participated in the study and the student鈥檚 score on the difficult questions is 20%. Which exam form is the student more likely to have taken, the blue or the red exam? Explain.

Parents Against Watching Television.A society called Parents Against Watching Television (PAWT) is primarily concerned with the amount of television viewed by today鈥檚 youth. It asked 300 parents of elementary school aged children to estimate the number of hours their child spent watching television in any given week. The mean and the standard deviation for their responses were 17 and 3, respectively. PAWT then constructed a stem-and-leaf display for the data, which showed that the distribution of the number of hours was a symmetric, mound-shaped distribution. Identify the interval where you believe approximately 95% of the television viewing times fell in the distribution.

Do social robots walk or roll? A social (or service) robot is designed to entertain, educate, and care for human users. In a paper published by the International Conference on Social Robotics (Vol. 6414, 2010), design engineers investigated the trend in the design of social robots. Using a random sample of 106 social robots obtained through a Web search, the engineers found that 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. This information is portrayed in the accompanying graph.

a. What type of graph is used to describe the data?

b. Identify the variable measured for each of the 106 robot designs.

c. Use the graph to identify the social robot design that is currently used the most.

d. Compute class relative frequencies for the different categories shown in the graph.

e. Use the results from part d to construct a Pareto diagram for the data.
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