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 20% 13% 21% 17% 20% 9%

Required:
Using the income midpoints x and the percent of super shoppers, do we have a valid probability distribution? Explain.

Yes. Using the income midpoints  x and the percent of super shoppers, we can conclude that we have a valid probability distribution.

Given:

Income ranges: 5-15, 15-25, 25-35, 35-45, 45-55, 55 or more.

Midpoints x:       10,     20,      30,      40,       50,      60

Percent of super shoppers: 20%, 13%, 21%, 17%, 20%, 9%.

A valid probability distribution has two must have properties:

Its probabilities are non-negative.

Its probabilities sum to 1.

In the given data, the percentages can be converted to probabilities by dividing by 100 as :

0.2, 0.13, 0.21, 0.17, 0.2, 0.09

None of the probabilities are negative.

All probabilities add up to 1

Thus, given distribution is a valid probability distribution.

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Yes, the probability distribution is valid.

Step-by-step explanation:

Given :

Income range ___ midpoint(x) ___ %

5 - 15 10 20%

15 - 25 20 13%

25- 35 30 21%

35 - 45 40 17%

45 - 55 40 20%

55 or more 50 9%

Yes, we do have a valid probability distributuon ; as the summation of the percentage values is equal to 100%