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	21%	15%	21%	16%	19%	8%

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

(d) 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 = thousands of dollars

Answer 1

Computational Table:

Xi	Percent of super shopper (Pi)	PiXi	Pi*Xi2
10	21% = 0.21	2.1	21
20	15% = 0.15	3	60
30	21% = 0.21	6.3	189
40	16% = 0.16	6.4	256
50	19% = 0.19	9.5	475
60	8% = 0.08	4.8	288
Total	1	32.10	1289

Total Probability = 1, Therefore Valid probability.

C)

Find Expected Income ()

   Thousand of dollars

d) Find Standard deviation:

Therefore,

V(X) = E(X²) - [E(x)]²

V(X) = 1289 - 32.1²

V(X) = 258.59

Therefore,

Thousand of dollars