Level 3: Distributions · Problem 45 of 87

Poisson: rescaling the rate

A statistics problem from Statisticsdrill. Solve it with one answer box, with a fresh sample on every attempt and the worked steps and spreadsheet function in the answer, and it is checked the moment you submit.

The task

Orders reach a small web shop at an average rate of 0.5 per hour, following a Poisson process. What is the probability that at least one arrives in the next 10 minutes? Round to 4 decimal places.

What this problem teaches

First scale the mean to the interval: λ = rate per hour × minutes / 60. Then P(at least one) = 1 - P(none) = 1 - e^(-λ).

A hint if you get stuck

First scale the mean to the interval: λ = rate per hour × minutes / 60. Then P(at least one) = 1 - P(none) = 1 - e^(-λ).