Question

1. Customers arrive at a local ice cream stand at an average rate of 16 per hour and follow a Poisson distribution.

a. What is the probability that two customers will arrive in the next 15 minutes?

b.What is the probability that 20 customers will arrive in the next hour?

c. What is the probability that 10 or fewer customers will arrive in the next hour?

d. What is the probability that more than 20 customers will arrive in the next hour?

Answer 1

a)

Here, λ = 4 and x = 2

As per Poisson's distribution formula $P(X=x)= \dfrac{\lambda^xe^{-\lambda}}{x!}$

We need to calculate P(X = 2)

P(X = 2) =$\dfrac {4^2e^{-4}}{2!}$

P(X = 2) = 0.1465

Ans: 0.1465

b)

P(X = 20) = 0.0559

=POISSON.DIST(20,16,FALSE)

c)

P(X $\leq$ 10) = 0.0774

=POISSON.DIST(10,16,TRUE)

d)

P(X > 20) = 1 - P(X $\leq 20$ )

=1 - POISSON.DIST(20,16,TRUE) 

P(X > 20) = 0.1318