A survey conducted by the Consumer Reports National Research Center reported, am

Question

A survey conducted by the Consumer Reports National Research Center reported, among other things, that women spend an average of 1.2 hours per week shopping online. Assume that hours per week shopping online are Poisson distributed. If this survey result is true for all women and if a woman is randomly selected,

a. What is the probability that she would shop exactly two hours online over a one-week period?
b. What is the probability that a woman would shop four or more hours online during a one-week period?
c. What is the probability that a woman would shop fewer than five hours in a three-week period?

Explanation / Answer

= 1.2

P(X = x) = e- * x / x!

a) P(X = 2) = e-1.2 * 1.22 / 2! = 0.2169

b) P(X > 4) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)]

                   = 1 - [e-1.2 * 1.20 / 0! + e-1.2 * 1.21 / 1! + e-1.2 * 1.22 / 2! + e-1.2 * 1.23 / 3! ]

                   = 1 - 0.9566

                   = 0.0338

c) = 1.2 * 3 = 3.6

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

               = e-1.2 * 3.60 / 0! + e-1.2 * 3.61 / 1! + e-1.2 * 3.62 / 2! + e-1.2 * 3.63 / 3! + e-1.2 * 3.64 / 4!

               = 0.7064

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