Question: Marketing: Age. 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 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 age group, use the midpoint 67 years.

1. Using the age midpoints x and the percentages of super shoppers, do we have a valid probability distribution? Explain.
2. Use a histogram to graph the probability distribution of part (a).
3. Compute the expected age p. of a super shopper.

   Age range, years	Midpoint x	Percent of super shoppers	x *p	(X-Xbar) 2
   18-28	23	7%	1.610	26.83635
   29-39	34	44%	14.960	32.39122
   40-50	45	24%	10.800	1.405536
   51-61	56	14%	7.840	25.2135
   62 and over	67	11%	7.370	65.597
   	Sum	100%	42.580	151.444

   
   Hence, the mean is \(\mu =42.58\)
4. Compute the standard deviation o- for ages of super shoppers.

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