A statistics department is holding alumni by telephone asking for donation to aid fund new computer laboratory. Past history describes that 40% of the alumni contacted in this manner will make the contribution of at least $100. A random sample of 20 alumni is chosen. Let X represents number of alumni which makes at contribution of at least $100.
a) Completely explain the probability distribution of X (name and parameters).
b) Find out the probability that exactly 9 alumni will make contribution of at least $100?
c) Find out the probability that at least 9 alumni will make contribution of at least $100?
d) How many alumni would you anticipate to make contribution of at least $100?
Find out the probability that at least 9 but not more than 12 will make contribution of at least $100?