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 50 customers. The dealer will be fined if the number of customers who report favorably is between 25 and 27. The dealership will be dissolved if fewer than 25 customers report favorably. It is known that 67% of the dealer’s customers report favorably on satisfaction surveys. [You may find it useful to reference the z table.]

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

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

Explanation / Answer

Solution:- Given that n = 50, p = 0.67

mean = n*p = 50*0.67 = 33.5

sd = sqrt(n*p*q) = sqrt(50*0.67*0.33) = 3.3249

a. P(25 < X < 27) = P((25 - 33.5)/3.3249 < (x - mu)/sigma < (27 - 33.5)/3.3249)

= P(-2.56 < Z < -1.96)

= 0.0198

b. P(X < 25) = P(Z < -2.56) = 0.0052

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.