A Statistics Department Is Contacting Alumni by Telephone and Asking

Essay

A statistics department is contacting alumni by telephone and 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 make a contribution of at least $50.
a. What is the probability that exactly 15 alumni will make a contribution of at least $50?
b. What is the probability that between 14 and 18 alumni, inclusively, will make a contribution of at least $50?
c. What is the probability that fewer than 17 alumni will make a contribution of at least $50?
d. What is the probability that more than 15 alumni will make a contribution of at least $50?
e. How many alumni would you expect to make a contribution of at least $50?