What is the income distribution of super shoppers (see Problem 8)? 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.

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

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