At least four Poisson arrivals in an hour

Question

Shoppers arrive at a store according to a Poisson process averaging $7$ per hour. To three decimal places, what is the probability that $4$ or more shoppers arrive during one particular hour?

Short answer

About $0.918$ . The count is $\text{Poisson}(7)$ , so subtract the first four terms: $1-e^{-7}\left(1+7+\tfrac{49}{2}+\tfrac{343}{6}\right)\approx1-0.0818=0.918$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Defining the Poisson Process: Three Equivalent Constructions
Expectation, Mean, and Variance
Conditional Expectation and Variance Revisited

Start with a free lesson: Expectation, Variance and Covariance is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free