Intact is the leading property and casualty (P&C) insurer in Canada and claimed 17% of the market in its “Quick Facts” report for 3Q14. The top five P&C insurers have 38% of the market. Suppose you work for a P&C insurer not currently in the top five, and you’d like to arrange focus groups with at least 75 customers of the top five companies, including at least 25 customers of Intact. You call at random a sample of 220 people in the market for P&C insurance.

a) What is the probability that your sample will contain at least 75 customers of the top five companies?

b) What is the probability that your sample will contain at least 25 customers of Intact?

c) What would be the effect of using a sample size of 20 and aiming to get smaller focus groups?