Question

Customers visit a restaurant at an average of 10 customers per hour a) Find the probability...

Customers visit a restaurant at an average of 10 customers per hour

a) Find the probability that exactly 15 customers visit the restaurant in a period of two hours

b) Find the probability that exactly 15 customers visit the restaurant in a period of two hours given that 5 have visited during the first hour

All information needed is provided.

Math   Statistics-And-Probability   
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Answer #1

The number of customers visiting the shop during a given time period has Poisson distribution.

The Poisson PMF is

a) The Poisson parameter for 2 hours is .

The probability that exactly 15 customers visit the restaurant in a period of two hours is

b) Divide the 2 hour interval into 2 independent 1 hour intervals. The Poisson parameter for 1 hour is .

We need to find the conditional probability,

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