Marketing: Income What is the income distribution of super shoppers (see Problem 10). In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars.

Income range 5–15 15–25 25–35 35–45 45–55 55 or more Midpoint x 10 20 30 40 50 60 Percent of super shoppers 21% 14% 22% 15% 20% 8%

(a) Using the income midpoints x and the percent of super shoppers, do we have a valid probability distribution? Explain.

(b) Use a histogram to graph the probability distribution of part (a).

(c) Compute the expected income m of a super shopper.

(d) Compute the standard deviation s for the income of super shoppers.