Suppose that 20% of all share market investors are retirees and we select a random sample of 25 share market investors.

a. If the random variable X is the number of investors in the sample who are retirees, provide two reasons why X has a binomial distribution.

b. State the value/s of parameter/s of X.

c. Calculate (using the appropriate statistical tables) the probability that between five and ten investors in the sample are retirees.

d. Calculate (using the appropriate statistical tables) the probability at least ten investors in the sample are retirees.

e. You have to explain to someone who has not studied statistics what this probability calculated in part d. means. Use simple non statistical language to explain this.

f. How many retirees would you expect to find in a random sample of 25 investors?