Question

Customers arrive at a rate of 24 people per hour to a bank. Assume that the number of customers arriving can be described using the Poisson distribution. What is the probability that at most 30 customers arrive in the next hour

Answer 1

0.90415

Explanation:

Given the following :

Arrival rate = mean(μ) = 24

Probability that at most 30 customers arrive in the next hour:

The poisson distribution formula :

P(x, μ) = [(e^-μ) * (μ^x)] / x!

Where :

e = euler's constant

P(x ⩽ 30) = p(0) + p(1) + p(2) +.... + p(30)

Using the online poisson probability distribution calculator :

P(x ⩽ 30, 24) = 0.90415

Therefore there is about 90.4% probability that at most 30 customers will arrive in the next hour.