What is the age distribution of promotion-sensitive shoppers? A supermarket supe

Question

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.

For the 62-and-over group, use the midpoint 67 years.

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

No. The events are distinct and the probabilities sum to 1.No. The events are indistinct and the probabilities sum to more than 1.    Yes. The events are distinct and the probabilities sum to 1.Yes. The events are indistinct and the probabilities sum to less than 1.Yes. The events are distinct and the probabilities do not sum to 1.

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

(c) Compute the expected age of a super shopper. (Round your answer to two decimal places.)
=  yr

(d) Compute the standard deviation for ages of super shoppers. (Round your answer to two decimal places.)
=  yr

Age range, years 18-28 29-39 40-50 51-61 62 and over Midpoint x 23 34 45 56 67 Percent of super shoppers 5% 40% 20% 9% 26% % Supr Shpers 20 23 34 45 56 67 Age

Explanation / Answer

a) Yes. The events are distinct and the probabilities sum to 1

b) top right curve is right:

c)

from above   = 46.21

d) standard deviation =14.42

x p(x) xP(x) (x-)2 (x-)2P(x) 23 0.050 1.150 538.704 26.935 34 0.400 13.600 149.084 59.634 45 0.200 9.000 1.464 0.293 56 0.090 5.040 95.844 8.626 67 0.260 17.420 432.224 112.378 total 1 = 46.21 1217.321 2= 207.8659 92.42 std deviation=     =    2 = 14.4176

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