What is the income distribution of super shoppers? Asupermarket 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.
(a) Using the income midpointsx and the percent of super shoppers, do we have a valid probability distribution? Explain.
a) Yes. The events are indistinct and the probabilities sum to less than 1.
b) Yes. The events are distinct and the probabilities sum to 1.
c) Yes. The events are distinct and the probabilities do not sum to 1.
d) No. The events are indistinct and the probabilities sum to 1.
e) 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).
(c) Compute the expected income μ of a super shopper. (Round your answer to two decimal places.)
μ = thousands of dollars
(d) Compute the standard deviation σ for the income of super shoppers. (Round your answer to two decimal places.)
σ = thousands of dollars
Extracted text: Income range Midpoint x Percent of super shoppers 5-15 15-25 25-35 35-45 45-55 55 or more 10 20 30 40 50 60 20% 13% 22% 17% 19% 9%
Extracted text: Maple Generated Plot 15 15 % Supr Shpprs 10 % Supr Shpprs 10 5- 10 20 30 40 50 60 10 20 30 40 50 60 Income Income 20 20 15 15 % Supr Shpprs 10 % Supr Shpprs 10 0T 10 30 40 60 10 20 40 50 60 Income Income 30 20 50 20 20