STATISTICS POISSON DISTRIBUTION WORKSHEET
This distribution describes the probability that x events occur within a
frame of time if there is a known mean for the number of events that
occur during that time frame.
𝑃(𝑥 ) =
𝜇 𝑥 𝑒 −𝜇
𝑥!
𝜎2 = 𝜇
1.) On average, three students visit me every day after school. Find the probability that today:
a.) Exactly three students will visit: ________
b.) No students will visit: ________
c.) More than two students will visit: ________
d.) What is the standard deviation? ________ (risk)
2.) A fast-food drive-thru serves an average of 5 customers per hour. Find the probability that the next
hour:
a.) Exactly four customers arrive: ________
b.) At least three customers arrive: ________
c.) At most four customers arrive: ________
d.) What is the standard deviation? ________
3.) A fisherman catches an average of 3 fish per hour. Find the probability that in the next hour, he
catches:
a.) No fish: ________
b.) Less than three fish: ________
c.) More than three fish: ________
d.) What is the standard deviation? ________
3b.) Suppose he fishes for 8 hours per day. Find the probability he catches somewhere between 20 and
25 fish (inclusive) tomorrow. (Hint: The mean is no longer 3!) ________
4.) A call center receives an average of four calls per minute. Find the probability that in the next
minute, the center will receive:
a.) Less than 3 calls ________
b.) More than 4 calls ________
c.) At most 5 calls ________
d.) What is the standard deviation? ________
4b.) What is the probability that exactly one call will arrive in the next 15 seconds? ________
4c.) What is the probability that no calls will arrive in the next 30 seconds? ________
Further thinking – The Poisson Distribution has more general applications. Instead of a time frame with
an unlimited amount of moments when Event E could occur, we can consider essentially unlimited
amounts of other things as well…
5.) Suppose that you are surrounded by 100 elephants, but you have a machine gun. Suppose you fire
the gun randomly and 200 bullets hit elephants (assume the ammo fired is essentially unlimited).
However, every elephant you don’t hit tramples you.
a.) What is the average number of hits per elephant? ______
b.) What is the probability an elephant avoids getting hit? ______
c.) You can expect to be trampled by how many elephants? ______
6.) An essentially unlimited number of bacteria are released into a culture containing 200 cells. 300
bacteria manage to infect cells, but they do so randomly (so that one cell might be infected by more
than one bacteria, and some might escape infection altogether).
a.) What is the average number of infections per cell? ______
b.) What is the probability that a cell avoids infection? ______
c.) What is the expected number of cells that avoid infection? ______
d.) What is the expected number of cells that have been infected with two bacteria? ________