The number of customers who make a purchase using a credit card at H&M; has the

Question

The number of customers who make a purchase using a credit card at H&M; has the following distribution where X = number of customers who use a credit card to make a purchase (It may be helpful to copy the numbers into Excel for faster calculations) (Round all answers to two decimal places) a) What is the probability that at least one but no more than three customers use a credit card to make a purchase? b) What is the probability that more than four customers will use a credit card to make a purchase? c) What is the expected number of customers who will use a credit card to make a purchase? d) What is the variance in the number of customers who will use a credit card to make a purchase?

Explanation / Answer

a) P(1 < X < 3) = P(X = 1) + P(X = 2) + P(X = 3)

                        = 0.15 + 0.29 + 0.35

                        = 0.79

b) P(X > 4) = 0

c) E(X) = 0 * 0.01 + 1 * 0.15 + 2 * 0.29 + 3 * 0.35 + 4 * 0.2 = 2.58

d) E(X2) = 02 * 0.01 + 12 * 0.15 + 22 * 0.29 + 32 * 0.35 + 42 * 0.2 = 7.66

Var(X) = E(X2) - (E(X))2 = 7.66 - 2.582 = 1.0036 = 1

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