Question

3. A plan for an executive traveler's club has been developed by an airline on the premise that 10% of its current customers would qualify for membership. (a) Assume the premise is valid. What is the chance that between 2 and 4 (in- clusive customers out of 25 randomly selected current customers qualify for membership? (b) Again assume the premise is valid. What is the expected number of customers who qualify and what is the standard deviation of the number who qualify in a random sample of 100 current customers?

Answer 1

a) n = 25

    p = 0.1

P(2 < X < 4)

= P(X = 2) + P(X = 3) + P(X = 4)

= 25C2 * (0.1)^2 * (0.9)^23 + 25C3 * (0.1)^3 * (0.9)^22 + 25C4 * (0.1)^4 * (0.9)^21

= 0.6308

b) Expected value = np = 100 * 0.1 = 10

   Standard deviation = sqrt(np(1 - p))

                               = sqrt(100 * 0.1 * 0.9)

                               = 3