What is the income distribution of super 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. 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 range5-1515-2525-3535-4545-5555 or moreMidpointx102030405060Percent of super shoppers20%15%20%16%19%10%

(a)Using the income midpointsxand the percent 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 distinct and the probabilities do not sum to 1.

No. The events are indistinct and the probabilities sum to 1.

Yes. The events are indistinct and the probabilities sum to less than 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). (Select the correct graph.)

(c)Compute the expected incomeof a super shopper (in thousands of dollars). (Enter a number. Round your answer to two decimal places.)

=thousands of dollars

(d)Compute the standard deviationfor the income of super shoppers (in thousands of dollars). (Enter a number. Round your answer to two decimal places.)

=thousands of dollars