Question

As reported by a recent survey, the fast-food resturaunt with the best drive-through time had a mean time spent in the drive-through of μ=64.3 seconds. Assuming drive-through times are normally distributed with σ=2.9 seconds, complete parts a through d below.

a. What is the probability that a randomly selected car will get through the drive-through in less than 60.5 seconds?

b. What is the probability that a randomly selected cad will spend more than 70.8 seconds in the drive-through?

c. What proportion of cars spend between 60.5 and 70.8 seconds in the drive-through?

d. Would it be unusual for a car to spend more than 70.8 seconds in the drive-through?

(multiple choice answers below)

a) No, because the probability of randomly choosing a car that waits more than 70.8 seconds in the drive-through is greater than 5%.

b) No, because the probability of randomly choosing a car that waits more than 70.8 seconds in the drive-through is less than 5%.

c) Yes, because the probability of randomly choosing a car that waits more than 70.8 seconds in the drive-through is less than 5%.

d) Yes, because the probability of randomly choosing a car that waits more than 70.8 seconds in the drive-through is greater than 5%.

Answer 1

Given that, mean = 64.3 seconds and

standard deviation = 2.9

a) We want to find, P(X < 60.5)

Therefore, required probability is 0.0951

b) We want to find, P(X > 70.8)

Therefore, required probability is 0.0125

c) We want to find, P(60.5 < X < 70.8)

Therefore, required probability is 0.8924

d) Since, P(X > 70.8) = 0.0125 < 0.05 it is unusual

Answer: c) Yes, because the probability of randomly choosing a car that waits more than 70.8 seconds in the drive-through is less than 5%