According to a survey conducted by TD Ameritrade, one out of four investors have exchange-traded funds in their portfolios (USA Today, January 11, 2007). Consider a sample of 20 investors.
a. Compute the probability that exactly 4 investors have exchange-traded funds in their portfolios.
b. Compute the probability that at least 2 of the investors have exchange-traded funds in their portfolios.
c. If you found that exactly 12 of the investors have exchange-traded funds in their portfolios, would you doubt the accuracy of the survey results?
d. Compute the expected number of investors who have exchange-traded funds in their portfolios.