Question: Suppose that the number of customers arriving each hour at the only checkout counter in a local pharmacy is approximately Poisson distributed with an expected arrival rate of 20 customers per hour.
a. Find the probability that exactly 10 customers arrive in a given hour.
b. Find the probability that at least five customers arrive in a given hour.
c. Find the probability that no more than 25 customers arrive in a given hour.
d. Find the probability that between 10 and 30 customers (inclusive) arrive in a given hour.
e. Find the largest integer k such that we can be at least 95% sure that the number of customers arriving in a given hour will be greater than k.
f. Recalling the relationship between the Poisson and exponential distributions, find the probability that the time between two successive customer arrivals is more then four minutes. Find the probability that it is less than two minutes.