Step 1 :The problem is asking for probabilities related to a normal distribution. The mean (mu) is 151.3 seconds and the standard deviation (sigma) is 27 seconds.
Step 2 :For part (b), we need to find the probability that a randomly selected car will spend more than 198 seconds in the restaurant's drive-through. This is equivalent to finding the area under the normal distribution curve to the right of 198 seconds.
Step 3 :For part (c), we need to find the proportion of cars that spend between 2 and 3 minutes (or 120 and 180 seconds) in the restaurant's drive-through. This is equivalent to finding the area under the normal distribution curve between 120 and 180 seconds.
Step 4 :For part (d), we need to find the probability that a car spends more than 3 minutes (or 180 seconds) in the restaurant's drive-through. This is equivalent to finding the area under the normal distribution curve to the right of 180 seconds.
Step 5 :The probability that a randomly selected car will spend more than 198 seconds in the restaurant's drive-through is approximately 0.0418. This is represented as \(\boxed{0.0418}\).
Step 6 :The proportion of cars that spend between 2 and 3 minutes in the restaurant's drive-through is approximately 0.7329. This is represented as \(\boxed{0.7329}\).
Step 7 :The probability that a car spends more than 3 minutes in the restaurant's drive-through is approximately 0.1439. Since this probability is greater than 0.05, it would not be unusual for a car to spend more than 3 minutes in the restaurant's drive-through. This is represented as \(\boxed{0.1439}\).