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You are a hostess at a restaurant. Employees are expected to complete inventory, clean, and lock...

You are a hostess at a restaurant. Employees are expected to complete inventory, clean, and lock the doors by 10:00 PM. The restaurant’s policy is to not seat anyone any time after 8:30 to meet this expectation. From examining the cameras and looking at previous data, it was discovered that on average 8 people come into the restaurant from 8:00 to 8:30 PM. (a) What is the probability that 5 people enter the restaurant from 8:00 to 8:30 PM? (b) Use tools to calculate the probability that more than 9 people enter the restaurant between 8:00 to 8:30 PM?

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Answer #1

Let X is a random variable shows the number of customers  come into the restaurant from 8:00 to 8:30 PM. Here X has Poisson distribution with parameter The pdf of X is

(a)

The probability that 5 people enter the restaurant from 8:00 to 8:30 PM is

Excel formula used: "=POISSON(5,8,FALSE)"

(b)

The probability that more than 9 people enter the restaurant between 8:00 to 8:30 PM is

Excel formula used: "=1-POISSON(9,8,TRUE)"

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