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. 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 8% 41% 19% 9% 23% 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. Yes. The events are distinct and the probabilities sum to 1. Yes. The events are indistinct and the probabilities sum to less than 1. No. The events are distinct and the probabilities sum to 1. Yes. The events are distinct and the probabilities do not sum to 1. No. The events are indistinct and the probabilities sum to more than 1. Correct: Your answer is correct.

(b) Use a histogram to graph the probability distribution of part (a). A graph has a horizontal axis labeled Age and a vertical axis labeled % Super Shoppers. The histogram has 5 bars. Each bar is associated with a label and an approximate value as listed below. 23: 23 34: 9 45: 19 56: 41 67: 8 A graph has a horizontal axis labeled Age and a vertical axis labeled % Super Shoppers. The histogram has 5 bars. Each bar is associated with a label and an approximate value as listed below. 23: 23 34: 19 45: 8 56: 9 67: 41 A graph has a horizontal axis labeled Age and a vertical axis labeled % Super Shoppers. The histogram has 5 bars. Each bar is associated with a label and an approximate value as listed below. 23: 8 34: 41 45: 19 56: 9 67: 23 A graph has a horizontal axis labeled Age and a vertical axis labeled % Super Shoppers. The histogram has 5 bars. Each bar is associated with a label and an approximate value as listed below. 23: 41 34: 23 45: 8 56: 19 67:

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

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

Answer 1

0.45000 0.40000 0.35000 0.30000 0.25000 0.20000 0.15000 0.10000 0.05000 0.00000 23 34 45 56 67 P(X=x)

c)

x	P(X=x)	xP(x)	x2P(x)
23	0.08000	1.84000	42.32000
34	0.41000	13.94000	473.96000
45	0.19000	8.55000	384.75000
56	0.09000	5.04000	282.24000
67	0.23000	15.41000	1032.47000
total		44.7800	2215.7400
	E(x) =μ=	ΣxP(x) =	44.7800
	E(x2) =	Σx2P(x) =	2215.7400
	Var(x)=σ2 =	E(x2)-(E(x))2=	210.4916
	std deviation=	σ= √σ2 =	14.5083

from above:

μ=44.78

σ =14.51