Chebyshev’s theorem states that “at least 1 

k 1

2

”

of the data of a distribution will lie within kstandard deviations of the mean.

a. Use the computer commands on page 101 to randomly generate a sample of 100 data from a uniform (nonnormal) distribution that has a low value of 1 and a high value of 10. Construct a histogram using class boundaries of 0 to 11 in increments of 1 (see the commands on pp. 61–62). Calculate the mean and the standard deviation using the commands found on pages 74 and 88; then inspect the histogram to determine the percentage of the data that fell within each of the 1, 2, 3, and 4 standard deviation intervals. How closely do these percentages compare to the percentages claimed in Chebyshev’s theorem and in the empirical rule?

b. Repeat part

a. Did you get results similar to those in part a? Explain.

c. Consider repeating part a several more times.

Are the results similar each time? If so, in what way are they similar?

d. What do you conclude about the truth of Chebyshev’s theorem and the empirical rule?