According to a survey conducted by Adi, one out of four investors have ETFs in their portfolios.. Consider a sample of 20 investors. [Hint: why is it that the random variable XBi(n, p)?]

a. Compute the probability that exactly four investors have ETFs in their portfolios.

b. Compute the probability that at least two of the investors have exchange-traded funds in their portfolios.

c. If you found that exactly 12 of the investors have ETFs in their portfolios, would you doubt the accuracy of the survey results?

d. Compute the expected number of investors who have ETFs in their portfolios.