Question

A bakery gets an average of 20 phone orders in a 2 hour time period. In order to find the probability that the bakery will get at most 2 phone orders in a 15 minute period using the Poisson distribution, what is the time interval of interest?

Answer 1

X ~ Poisson ()

Where = 20 orders in 2 hours (OR 120 minutes)

We have to find for time interval of 15 minutes.

t = 15/120 * 20 = 2.5 (this means 2.5 orders per 15 minutes)

P(X) = e^-t * (t)^X / X! , Where X = 0 , 1 , 2

P(X <= 2) = e^-2.5 + e^-2.5 * 2.5 + e^-2.5 2.5² / 2!

= 0.5438