What is the age distribution of promotion-sensitive shoppers? Asupermarket super shopperis defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon. (see chart below)

Age range, years -------------------18-28 | 29-39 | 40-50 | 51-61 | 62 and over

Midpointx ----------------------------- 23 | 34 | 45 | 56 | 67

Percent of super shoppers----------10% | 41% | 23% | 11% | 15%

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

(a)

Using the age midpointsxand the percentage of super shoppers, do we have a valid probability distribution? Explain.

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

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

(c) Compute the expected ageof a super shopper. (Round your answer to two decimal places.)

• =yr

(d)

Compute the standard deviationfor ages of super shoppers. (Round your answer to two decimal places.)

• =yr