4. [-/0.38 Points] DETAILS BBUNDERSTAT12 5.1.007.MI. Consider the probability distribution shown below. X 0 P(x) 0.25 0.45 Compute the expected value of the distribution. Compute the standard deviation of the distribution. (Round your answer to four decimal places.) Need Help? Rand Master 5. [0.09/0.38 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 5.1.010.MIS. 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 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% 45% 25% 13% 9% LA USE SALT 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 indistinct and the probabilities sum to less than 1. 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 do not sum to 1. . Yes. The events are distinct and the probabilities sum to 1. (b) Use a histogram to graph the probability distribution of part (a). (Because the data table has summarized the data Into categories, use SALT to create a bar chart.) (c) Compute the expected age , of a super shopper. (Round your answer to two decimal places.) yr (d) Compute the standard deviation s for ages of super shoppers. (Round your answer to two decimal places.) yr