What is the income distribution of super shoppers? A supermarket super shopper i

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.

(c) Compute the expected income of a super shopper. (Round your answer to two decimal places.)

(d) Compute the standard deviation for the income of super shoppers. (Round your answer to two decimal places.)

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 21% 13% 20% 17% 18% 11%

Explanation / Answer

c. In order to find the mean (expectation) of the given distribution, we will use the following formula:

=xp(x)

So, first we need to multiply each value of X by each probability P(X), then add these results together. In this example we have:

=100.21+20*0.13+30*0.20+0.40*0.17+50*0.18+60*0.11=33.1

d. In order to find the standard deviation of the given distribution, we will use the following formula:

=sqrt(x2p(x)2)

x2p(x)=1371

=sqrt(x2p(x)2)=sqrt(1371(33110)2)=16.5949

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