Cars arrive at the Wendy's drive-through at a rate of 1 car every 5 minutes between the hours of 11:00 PM and 1:00 AM. on Saturd

Question

2 months ago

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Cars arrive at the Wendy's drive-through at a rate of 1 car every 5 minutes between the hours of 11:00 PM and 1:00 AM. on Saturd

ay nights. Wendy's begins an advertising blitz that touts its late-night drive-through service and convenience. After one week of advertising, the Wendy's marketing department conducts a survey at 200 Wendy's to count the number of cars, X, that arrive at the drive-through between the hours of 12:00 midnight and 12:30 AM on Saturday night.
Question 1. Use the Poisson distribution to calculate the probability that exactly 8 cars will use the drive-through between 12:00 midnight and 12:30 AM on a Saturday night at Wendy's. Do the same for exactly 9 cars.

P(X = 8) (use 4 decimal places)
P(X = 9) (use 4 decimal places)

Question 2. At how many of the 200 restaurants in the survey would you expect exactly 8 customers to use the drive-through? exactly 9 customers?

expected number of 200 restaurants in which exactly 8 customers use the drive-through.
expected number of 200 restaurants in which exactly 9 customers use the drive-through.

Mathematics

1 answer:

Zina [12.3K] · Answer 1 · 2026-03-14T10:19:56+03:00

1) For the expected number in 200 restaurants where exactly 8 customers use the drive-through, it is 20.66. Similarly, for exactly 9 customers, the expected count is 13.76. To compute these expectations, we utilize the Poisson distribution which defines the success probability X, considering a certain operational rate for the drive-through services during specified times.