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%22%17%20%6%

(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 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.

No. The events are indistinct and the probabilities sum to 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

4.

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A particular lake is known to be one of the best places to catch a certain type of fish. In this table,x= numberof fish caught in a6-hourperiod. The percentage data are the percentages of fishermen who caughtxfishin a6-hourperiod while fishing from shore.

x01234 or more%43%35%15%6%1%

(a)Convert the percentages to probabilities and make a histogram of the probability distribution. (Select the correct graph.)

(b)Find the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6-hour period. (Enter a number. Round your answer to two decimal places.)

(c)Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6-hour period. (Enter a number. Round your answer to two decimal places.)

(d)Compute, the expected value of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to two decimal places.)

=fish

(e)Compute, the standard deviation of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to three decimal places.)

=fish