The mean and the standard deviation of the sample of 65 customer satisfaction ratings are and = 42.95 and s = 2.6424.
a. What does the histogram in Figure 2.15 say about whether the Empirical Rule should be used to describe the satisfaction ratings?
b. Use the Empirical Rule to calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all possible satisfaction ratings.
c. Does the estimate of a tolerance interval containing 99.73 percent of all satisfaction ratings provide evidence that 99.73 percent of all customers will give a satisfaction rating for the XYZ-Box game system that is at least 35 (the minimal rating of a "satisfied" customer)? Explain your answer.
d. How do the percentages of the 65 customer satisfaction ratings in Table 1.7 that actually fall into the intervals [± s], [±2s], and [± 3s] compare to those given by the Empirical Rule?
Do these comparisons indicate that the statistical inferences you made in parts b and c are reasonably valid?
Figure 2.15

Table 1.7

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RatingF Histogram of Video Game Ratings 2 36 3 38 4 40 5 42 8 44 20 16 46 848 9 More 15 12 10 13 36 38 42 More Rating Upper Class Boundary Composite Scores for the Video Game Satisfaction Rating Case TABLE 1.7 39 45 38 42 42 46 45 45 46 43 47 43 41 40 43 42 42 47 43 45 46 45 47 46 48 38 42 46 43 45 45 41 45 40 39 40 42 45 46 41 43 39 43 41 38 43 36 39 41