Twelve percent of single women in the kingdom have feet which will fit into a gl

Question

Twelve percent of single women in the kingdom have feet which will fit into a glass slipper. Prince Charming thinks he must continue finding women who fit such a slipper, so that he has a collection to choose from. He would like 10 women who fit the slipper to compete on a “Bachelor”-type show for his hand in marriage.

a) How many women should he expected to have to check until he finds 10 women who fit the glass slipper?

b) What is the standard deviation of the number of women that he will have to find until he finds 10 women who fit the glass slipper?

Explanation / Answer

Let

   X1 be the number of trials to the first success,

   X2 be the number of additional trials to the second success,

  X3 be the number of additional trials to the third success

Each Xi is a geometric variable with success factor p; so, E(Xi)=1/p; for each i.

Now let Y be the number of trials to the xth success. Note that

Y is a negative binomial random variable.

Recalling that the expectation of a sum of random variables is the sum of their expectations:

x = 10, p = 0.12, E(Y) = 10/0.12 = 83.333 = 83

b) Variance is given by

Var(Y) = [x*(1-p)/p2] = [10*(1-0.12)/0.122] = 611.11

SD(Y) = sqrt(Var(Y)) = sqrt(611.11) = 24.72

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.