1. Fast food restaurants spend time studying the amount of time cars spend in th
ID: 3042159 • Letter: 1
Question
1.
Fast food restaurants spend time studying the amount of time cars spend in their drive-through. QSR Magazine studies drive through times each year. Wendy’s has the fastest drive through time with an average of 133.63 seconds in the most recent study. Answer these questions below assuming drive through times are normally distributed with a standard deviation of 28 seconds.
a. What is the probability that a randomly selected car will get through Wendy’s drive-through in less than 100 seconds?
b. What percentage of people will have spent more than 160 seconds in the drive through?
c. What percentage of cars spend between 2 and 3 minutes in the drive through?
d. Would it be unusual for a car to spend more than 3.5 minutes in Wendy’s drive-through? Why?
Explanation / Answer
Average fastest drive trhough time = 133.63 seconds
Standard deviation fastest drive through time = 28 seconds
(a0 Here X is the fastest drive through time for an random driver.
Pr(X < 100 seconds) = NORM (X < 100 seconds ; 133.63 seconds, 28 seconds)
Z = (100 - 133.63)/28 = -1.20
Pr(X < 100 seconds) = Pr(Z < -1.20 ) = 0.1149
(b) Pr(X > 160 seconds) = 1 - Pr(X < 160 seconds) = 1- NORM (X > 160 seconds; 133.63 seconds, 28 seconds)
Z = (160 - 133.63)/28 = 0.942
Pr(X > 160 seconds) = 1 - Pr(Z < 0.942) = 1 - 0.8269 = 0.1731
(c) Pr(120 seconds < X < 180 seconds) = NORM (X < 180 Seconds) - NORM(X < 120 seconds) = (Z2) - (Z1)
where is standard normal cumulative distribution.
Z2 = (120 - 133.63)/28 = - 0.4868
Z1 = (180 - 133.63)/28 = 1.656
Pr(120 seconds < X < 180 seconds) = Pr(Z < 1.656) - Pr(Z < -0.4868) = 0.9511 -0.3132 = 0.6380
(d) Here 3.5 minutes means 210 seconds
So we will check probability that a car will spend 210 seconds or more in drive through
Pr(X > 210 seconds) = 1 - Pr(X < 210 seconds)
Z = (210 - 133.63)/ 28 = 2.7275
Pr(X > 210 seconds) = 1 - Pr(Z < 2.7275) = 1 - 0.9968 = 0.0032
as this probability is very much less than 0.05 so it is quite unusual that for a car to spend more than 3.5 minutes in Wendy’s drive-through
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.