Question

Wendy’s Drive-Through Fast-food restaurants spend quite a bit of time studying the amount of time cars spend in their drive-throughs. Certainly, the faster the cars get through the drive-through, the more the opportunity for making money. QSR Magazine studied drive-through times for fast-food restaurants and found Wendy’s had the best time, with a mean time spent in the drive-through of 138.5 seconds. Assuming drive-through times are normally distributed with a standard deviation of 29 seconds, answer the following.

(a) What is the probability that a randomly selected car will get through Wendy’s drive-through in less than 100 seconds? In other words, find P(X < 100).

Answer 1

0.09885

Explanation:

Given that Wendy’s Drive-Through Fast-food restaurants spend quite a bit of time studying the amount of time cars spend in their drive-throughs. Certainly, the faster the cars get through the drive-through, the more the opportunity for making money. QSR Magazine studied drive-through times for fast-food restaurants and found Wendy’s had the best time, with a mean time spent in the drive-through of 138.5 seconds.

Std deviation = 29 seconds (population stddev)

Let X be the time cars spend in their drive-throughs.

X is N(138.5, 29)

a) the probability that a randomly selected car will get through Wendy’s drive-through in less than 100 seconds

=
`P(X<100)\\`

=
`P(Z<-38.5/29)\\\\==0.09885`