Question

Choose the correct problem formulation: A Statistics Department is contacting alumni by telephone asking for donations to help fund a new computer laboratory. Past history shows that 80% of the alumni contacted in this manner will make a contribution of at least $50. A random sample of 20 alumni is selected. Let x represent the number of alumni that makes a contribution of at least $50. What is the probability that exactly 15 alumni will make a contribution of at least $50

Answer 1

Answer:

0.1745

Step-by-step explanation:

We are given the following information:

We treat alumni contacted by telephone making a contribution of at least $50 as a success.

P(Alumni making a contribution) = 80% = 0.8

Then the number of alumni follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Sample size, n = 20

We have to evaluate:

$P(x = 15)\\= \binom{20}{15}(0.8)^{15}(1-0.8)^5\\=0.1745$

Thus, 0.1745 is the probability that exactly 15 alumni will make a contribution of at least $50 when contacted by telephone.