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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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