Question

A car manufacturer is concerned about poor customer satisfaction at one of its dealerships. The management decides to evaluate the satisfaction surveys of its next 50 customers. The dealer will be fined if the number of customers who report favorably is between 29 and 41. The dealership will be dissolved if fewer than 29 customers report favorably. It is known that 71% of the dealer’s customers report favorably on satisfaction surveys.

a. What is the probability that the dealer will be fined?

Answer 1

P(a customer report favorably), p = 0.71

q = 1 - 0.71 = 0.29

n = 50

P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = np

= 50 x 0.71

= 35.5

Standard deviation =

=

= 3.21

a) P(the dealer will be fined) = P(29 X 41)

= P(X < 41.5) - P(X < 28.5) {with continuity correction}

= P(Z < (41.5 - 35.5)/3.21) - P(Z < (28.5 - 35.5)/3.21)

= P(Z < 1.87) - P(Z < -2.18)

= 0.9693 - 0.0146

= 0.9547