10 Consider a shop where customers arrive at random at a rat

10. Consider a shop where customers arrive at random at a rate of twenty persons per hour. What is the probability that the time intervals between successive arrivals will be: (a) shorter than 3 minutes, (b) longer than 4 minutes (c) Suppose that that 10% of the customers buy an item. Find the distribution of the number of customers who buy an item in an hour

Solution

We need to use the poisson distribution with lamba=20, which is 1 every 3 minutes.

A. find P(X<20) because that would be one customer every 3 minutes. Using poissoncdf(20, 20) on a calculator=.5591

B. Find P(X>15) because that would be one customer every 4 minutes. Using poissoncdf(20, 15)=.1565. Then subtract from 1 because we want greater than=.8435

C. If 10% of customers buy an item, there would be a poisson distribution lamba=2 of customers who buy an item an hour.