Question

4. 6.55/12.5 points Previous Answers BBUnderStat 12 5.1.011. 2/10 Submissions Used My Notes Ask Your Teacher 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. | 5-15 15-25 25-35 35-4545-55 SS or more 10 20 30 40 50 Lercent super shooge 2 1 3% 272 (a) Using the income midpoints x and the percent of super shoppers, do we have a valid probability distribution? Explain. Yes. The events are indistinct and the probabilities sum to less than 1. O No. The events are indistinct and the probabilities sum to l. Yes. The events are distinct and the probabilities do not sum to 1. No. The events are indistinct and the probabilities sum to more than 1. Yes. The events are distinct and the probabilities sum to 1. (b) Lise a histogram to graph the probability distribution of part (a). (c) Compute the expected income of a super shopper (Round your answer to two decimal places.) - thousands of dollars (d) Compute the standard deviation for the income of super shoppers. (Round your answer to two decimal places.) thousands of dollars Need Help? Read It Walisht

Answer 1

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a. The probabilities if they add up to 1, then its a valid probability distribution
Yes, they add up to .21+.13+.22+.16+.19+.09 = 1
Events are also distinct

So, Last option is correct

b. Lower right graph is correct

c. is E(x) = $32.60 and d. Stdev is $16.22 ( both in $'000)

p(x) E(x) E(x^2) [x^2 32.6 T Var(x) = E(x^2) - E(x)^2 Stdev(x) = sqrt(Var(x)) 263.24 16.22 10 1326 0.21 0.13 0.22 0.16 0.19 0.09 100 400 900 1600 2500 60 36001