An American Association of Individual Investors (AAII) survey found that 25% of AAII members had purchased shares of stock directly through an Initial Public Offering (IPO). From a random sample of 15...

An American Association of Individual Investors (AAII) survey found that 25% of AAII members had purchased shares of stock directly through an Initial Public Offering (IPO). From a random sample of 15 AAII members, (Give answers to four decimal places.)

a) what is the probability that exactly 5 had purchased IPO’s?

b) what is the probability that between 2 and 7 had purchased IPO’s?

c) what is the probability that at least 3 had purchased IPO’s?