A team of consultants working for a large national supermarket chain based in the New York metropolitan area developed a statistical model for predicting the annual sales of potential new store locations. Part of their analysis involved identifying variables that influence store sales, such as the size of the store (in square feet), the size of the surrounding population, and the number of checkout lanes. They surveyed 52 supermarkets in a particular region of the country and constructed the relative frequency distribution shown below to describe the number of checkout lanes per store, x.

a. Why do the relative frequencies in the table represent the approximate probabilities of a randomly selected supermarket having x number of checkout lanes?
b. Find E(x) and interpret its value in the context of the problem.
c. Find the standard deviation of x.
d. According to Chebyshev's Rule (Chapter 2, p. 80), what percentage of supermarkets would be expected to fall within μ ± σ? Within μ ± 2σ?
e. What is the actual number of supermarkets that fall within μ ± σ? μ ± 2 σ? Compare your answers with those of part d. Are the answers consistent?

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5 6 7 8 9 10 1 2 3 4 Relative Frequency 01 .04 .04 .08 .10 .15 25 .20 .08 .05