A car manufacturer is concerned about poor customer satisfaction at one of its d

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 62 customers. The dealer will be fined if the number of customers who report favorably is between 45 and 50. The dealership will be dissolved if fewer than 45 report favorably. It is known that 84% of the dealer’s customers report favorably on satisfaction surveys. Use Table 1.

a. What is the probability that the dealer will be fined? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probability ________

b. What is the probability that the dealership will be dissolved? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)
Probability ___________

Explanation / Answer

a)

X - number of customer who report favorably

X follow binomial distribution with n = 62 , p = 0.84

P(45 <= X <= 50)

= P(X<= 50) - P(X<= 44)

= 0.28279 - 0.007024

= 0.275766

b) P(X > 50)

= 1 - P(X <= 50)

= 0.7172091077

using normal approximation

mean = np = 62 *0.84 = 52.08

sd = sqrt(npq) = 62 *0.84*0.16 = 8.3328

P(45 <= X<= 50)

= P(44.5 < X< 50.5)

= P(-90966 <Z< -0.18961)

= 0.2433

b) P(X> 50)

= P(X>50.5)

= P(Z > -0.18961)

= 1 - 0.424807

= 0.5752

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