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.
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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