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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 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.

Answer :

FICHOHGO

Answer:

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%

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

[tex]0.2 + 0.13 + 0.21 + 0.17 + 0.2 + 0.09 = 1[/tex]

Thus, given distribution is a valid probability distribution.

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