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Answer:
1)
2) Expected number of 200 restaurants in which exactly 8 customers use the drive-through: 20.66
Expected number of 200 restaurants in which exactly 9 customers use the drive-through: 13.76
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
is the Euler number
is the mean in the given time interval.
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.
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 Saturday nights. This means that during 30 minutes, 6 cars expected to arrive. So .
P(X = 8)
P(X = 9)
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?
There is a 10.33 probability that 8 customers would use the drive through for each restaurant.
So of 200, the expected number is
There is a 6.88 probability that 9 customers would use the drive through for each restaurant.
So of 200, the expected number is