Prince Charming has to go around town asking if the glass slipper fits until he

Question

Prince Charming has to go around town asking if the glass slipper fits until he finds a woman whose foot fits properly in the slipper so that he will know who to marry. The probability of a glass slipper fitting a randomly selected woman is 0.12, and the probabilities are independent for the various women. Let X be the number of women he has to visit until he finds a woman who fits the shoes. Assume that there are an unlimited supply of eligible women in the town.

c) What is the expected number of women he will have to try?

d) What is the standard deviation of the number of women he will have to try?

Explanation / Answer

p = 0.12

This is a geometric distribution

a) expected value = 1/p

                          = 1/0.12

                         = 8.33 or 8 (approx)
b) variance = (1 - p)/p2

                = (1 - 0.12) / 0.122

                = 61.11

standard deviation = sqrt(61.11) = 7.82 or 8 (approx.)

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