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 5% 42% 18% 12% 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. (b) Use a histogram to graph the probability distribution of part (a). (c) Compute the expected age of a super shopper. (d) Compute the standard deviation or for ages of super shoppers. Step 1 (a) Using the age midpoints x and the percentage of super shoppers, do we have a valid probability distribution? Explain. In order to have a valid probability distribution, 2 conditions must be met. 1. The probability distribution has a probability assigned to each distinct value of the random variable. 2. The sum of all the assigned probabilities must be 1. We can see from the table that each distinct value of the random variable has been assigned a probability. Use these probabilities to check if the sum of all the assigned probabilities is equal to 1. P(x) = P(23) + P(34) + P(45) + P(56) + P(67) = 0.05 +0.42 + 0.18 + 0.12 + = 1