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 dealership 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 dealership's customers report favorably on satisfaction surveys. [You may find it useful to reference the z table.) a. What is the probability that the dealership will be fined? (Round "x" value to 4 decimal places, and final answer to 4 decimal places.)

Answer 1

To find the probability that the dealership will be fined, you need to use the binomial probability formula and the z-table.

Step-by-step explanation:

To find the probability that the dealership will be fined, we need to determine the number of customers who report favorably within the specified range of 25 to 27.

First, we find the probability of exactly 25 customers reporting favorably using the binomial probability formula:

P(X=25) = (50 choose 25) * (0.67^25) * (0.33^25)

Next, we find the probability of exactly 26 customers reporting favorably using the same formula:

P(X=26) = (50 choose 26) * (0.67^26) * (0.33^24)

Finally, we find the probability of exactly 27 customers reporting favorably:

P(X=27) = (50 choose 27) * (0.67^27) * (0.33^23)

The probability that the dealership will be fined is the sum of these three probabilities:

P(fined) = P(X=25) + P(X=26) + P(X=27)

Using the z-table, we can convert these probabilities to z-scores and find the area under the standard normal curve to get the final probability.