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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’s 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=120×96 + 93 +....+ 95 + 91X-=179120X-= 89.55S =1n-1∑i=1nx1-x¯2=119∑i=1nx1-2=4.71811

02

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

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

03

(b) Chebyshev’s

Chebyshev’s rule,

P1×x-μ⩾Kσ⩽1K2P1×x-μ⩾Kσ⩾1-1K2P1x-89.55⩽15⩾1-1P1x-89.55⩽15⩾0P1x-89.55⩽25⩾1-14P1x-89.55⩽25⩾0.75P1x-89.55⩽35⩾1-19P1x-89.55⩽35⩾0.889

Yes, it agrees with Chebyshev’s rule,

The empirical rule is,

x¯±σis 68%x¯±2σis 95%x¯±3σis 99.7%

The empirical rule is also satisfied.

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Most popular questions from this chapter

Hotels’ use of ecolabels.Ecolabels such as Energy Star, Green Key, and Audubon Internationalare used by hotels to advertise their energy-saving and conservation policies. The Journal of Vacation Marketing(January 2016) published a study to investigate how familiar travelers are with these ecolabels and whether travelers believe they are credible. A sample of 392 adult travelers were administered a questionnaire. One question showed a list of 6 different eco-labels, and asked, “How familiar are you with this ecolabel, on a scale of 1 (not familiar at all) to 5 (very familiar).” Summarized results for the numerical responses are given in the table.

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Ecolabel

Mean

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Energy Star

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b.All 70 car body defects were further classified as to type. The frequencies are provided in the following table. Form a Pareto diagram for the type of body defect. (Adding this graph to the original Pareto diagram of part a is called exploding the Pareto diagram.) Interpret the result. What type of body defect should be targeted for special attention?

Body Defect

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Hour

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125

148

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Descriptive Statistics: Ratings

Results for Prize = Job

Variable

Degree

N

Mean

StDev

Minimum

Maximum

Rating

First

54

7.796

4.231

1.000

17

None

35

7.457

4.388

1.000

20

Post

10

9.80

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2.000

17

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Degree

N

Mean

StDev

Minimum

Maximum

Rating

First

33

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10.62

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a.Give a practical interpretation of the mean rating for contestants with a first (bachelor’s) degree who competed for a job with Lord Sugar.

b.Find an interval that captures about 95% of the ratings for contestants with a first (bachelor’s) degree who competed for a job with Lord Sugar.

c.An analysis of the data led the researchers to conclude that “when the reward for winning . . . was a job, more academically qualified contestants tended to perform less well; however, this pattern is reversed when the prize changed to a business partnership.” Do you agree? Explain.
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