What is the age distribution of promotion-sensitive shoppers? A supermarket super shopper is defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon. The following table is based on information taken from Trends in the United States (Food Marketing Institute, Washington, D.C.):

For the 62-and-over group, use the midpoint 67 years.
(a) Using the age 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 age m of a super shopper.
(d) Compute the standard deviation s for ages of super shoppers.

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18-28 29-39 40-50 51-61 62 and over Age range, years Midpoint x Percent of super shoppers 23 34 45 56 67 7% 44% 24% 14% 11%