Question

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 range 5-15 15-25 25-35 35-45 45-55 55 or more Midpoint x 10 20 30 40 50 60 Percent of super shoppers 22% 15% 22% 17% 18% 6% (a) Using the income midpoints x and the percent of super shoppers, do we have a valid probability distribution? Explain. No. The events are indistinct and the probabilities sum to more than 1. (b) Compute the expected income μ of a super shopper (in thousands of dollars). (Enter a number. Round your answer to two decimal places.) μ = [expected income in thousands of dollars] (c) Compute the standard deviation σ for the income of super shoppers (in thousands of dollars). (Enter a number. Round your answer to two decimal places.) σ = [standard deviation in thousands of dollars]

          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 range
5-15
15-25
25-35
35-45
45-55
55 or more

Midpoint x
10
20
30
40
50
60

Percent of super shoppers
22%
15%
22%
17%
18%
6%

(a) Using the income midpoints x and the percent of super shoppers, do we have a valid probability distribution? Explain.
No. The events are indistinct and the probabilities sum to more than 1.

(b) Compute the expected income μ of a super shopper (in thousands of dollars). (Enter a number. Round your answer to two decimal places.)
μ = [expected income in thousands of dollars]

(c) Compute the standard deviation σ for the income of super shoppers (in thousands of dollars). (Enter a number. Round your answer to two decimal places.)
σ = [standard deviation in thousands of dollars]

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Added by Madison G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert David Nguyen

07/30/2022

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Step 1: Calculate the expected income of a super shopper. Show more…

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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 range 5-15 15-25 25-35 35-45 45-55 55 or more Midpoint x 10 20 30 40 50 60 Percent of super shoppers 22% 15% 22% 17% 18% 6% (a) Using the income midpoints x and the percent of super shoppers, do we have a valid probability distribution? Explain. No. The events are indistinct and the probabilities sum to more than 1. (b) Compute the expected income μ of a super shopper (in thousands of dollars). (Enter a number. Round your answer to two decimal places.) μ = [expected income in thousands of dollars] (c) Compute the standard deviation σ for the income of super shoppers (in thousands of dollars). (Enter a number. Round your answer to two decimal places.) σ = [standard deviation in thousands of dollars]

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Transcript

00:01 Hi, i'm david and i'm here to have you and see your question.

00:04 Now let me bring up your question here.

00:06 In the question here we are given the table of the probability for the x and let me draw the table again here.

00:16 We will have this will be here, this will be the class and this will be the mid form and this will be the percentage and we have the class here it will be between the five, to the 15 and then the midpoint it will equal to the 10 and the percentage will be the 21 % which is 0 .21 so a condition will be the probability of the x and we call this will be the x will be the midpoint and then the next one i will have the 15 to the 25 and the midpoint equal to the 20 the 20 the percentage equals to 014 and then the next one will be the 25 to the 35 we have the midpoint equal to the 30 percentage equal to 0 and then the 35 to the 45 the midpoint will be the 40 percent it equal to the 0 point 17 and then from 45 to the 55 the midpoint will be the 50 and then we have the 0 .18 and 55 to the 5 to the 65, the midpoint equal to the 60, and we have this one will be the 0 .10, and i think that will be on the data given.

01:55 And from here the question a asked me to find the mean, denoted by the mule, and by the formula equal to the summation of the x times the problem to the x for own x.

02:07 Therefore we have to multiply them like a pair here and then we add them up.

02:14 Therefore we have the 10 times with the 0 .21 plus the 20 times in the 0 .14 plus the 30 times with the 0 .20 times with the 0 .20 plus the 30 times with the 0 .17.

02:29 And then plus 50 times with the 0 .118 plus 60 times the 0 .10.

02:39 And if we compute it, we will have, it will equal to 1 plus 20 times 0 .14 plus 30 times 0 .20, plus 40 times 0 .17, plus 50 times 0 .17, plus 50 times 0 .17, plus 50 times 0 .18, plus 60 times 0 .17, plus 50 times 0.

02:59 1, the vat equal to the 32 .7.

03:06 And that will be the mean.

03:08 The next question asked let you find the standard deviation...

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