Market research indicates that 40% of retirees would be interested in the services of an investment advisor if they were approached. An analyst at an investment advisory firm in a regional city is interested to see if this advice seems applicable to their potential clients. Accordingly the analyst intends to approach a sample of 20 local retirees to see how many are interested in their advisory services. The analyst uses the random variable X to represent the number in the sample who indicate they are interested in the firm's services.

a. State the possible values that the variable X may take in this instance.

b. State the type of distribution X has and the parameter/s for this distribution

c. Determine the expected value of X and interpret this value.

d. Calculate (using the appropriate statistical tables) the probability that between five (5) and eleven (11) retirees would be interested in investment services

It turned out that only 2 of the retirees approached indicated that they would be interested in the firm's services.

e. Determine P(X=2) using the appropriate probability distribution function (formula).