Suppose that X, 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 X is exactly 10.
b. Find the probability that X is at least 5.
c. Find the probability that X is no more than 25.
d. Find the probability that X is between 10 and 30 (inclusive).
e. Find the largest integer k such that we can be at least 95% sure that X 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 than four minutes. Find the probability that it is less than two minutes.