What is the income distribution of super 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. In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars. Income ran e 5-15 15-25 25-35 35-45 45-55 55 or more Mid int x 10 20 30 40 50 60 Percent of super shoppers 22% 13% 22% 16% 18% 9% (a) Using the income midpoints X and the percent of super shoppers, do we have a valid probability distribution? Explain. O No. The events are indistinct and the probabilities sum to more than 1. 0 Yes. The events are distinct and the probabilities do not sum to 1. 0 Yes. The events are distinct and the probabilities sum to 1. O No. The events are indistinct and the probabilities sum to 1. 0 Yes. The events are indistinct and the probabilities sum to less than 1. (b) Use a histogram to graph the probability distribution of part (a). (Select the correct graph.) 25 t 20 15 TTT % Supr Shpprs 10 TTT TTTTTT 10 20 30 40 50 60 O Income 25 20 15 ITTTTTTTTTT % Supr Shpprs 10 H 10 20 30 40 50 60 O Income\f(c) Compute the expected income I4 of a super shopper (in thousands of dollars). (Enter a number. Round your answer to two decimal places.) [4 = thousands of dollars (d) Compute the standard deviation 5 for the income of super shoppers (in thousands of dollars). (Enter a number. Round your answer to two decimal places.) 0' = thousands of dollars