A supermarket\'s market research team determines that among the set of customers

Question

A supermarket's market research team determines that among the set of customers purchasing

diapers, the number of bottles of whiskey purchased is a random variable, X, following the distribution

below:

x          p(x)

0          .05

1           .1

2          .15

3           .4

4          .2

5          .1

a. Determine the expected value of X.

b. Determine the variance and standard deviation of X.

c. What is the probability that at least 3 bottles of whiskey are purchased by a customer in this segment?

Explanation / Answer

a) E(x) = 0*.05+1*.1+2*.15+3*.4+4*.2+5*.1 = 2.9

b) variiance x = (.05*(0-2.9)^2)+(.1*(1-2.9)^2))+(.15*(2-2.9)^2)+(.4*(3-2.9)^2)+(.2*(4-2.9)^2)+(.1*(5-2.9)^2) = 1.59

SD = 1.59^.5 = 1.26

c) P = .4+.2+.1 = .7

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