Question

on average 5 people enter the retaurant per minute. what is the probability that more than 25 people enter the restaurant in the next 4 minutes?

Answer 1

On average 5 people enter the restaurant per minute. What is the probability that more than 25 people enter the restaurant in the next 4 minutes?

The above discussed distribution is a Poisson distribution with below attributes

A Poisson experiment is a statistical experiment that has the following properties:

• The experiment results in outcomes that can be classified as successes or failures.
• The average number of successes (μ) that occurs in a specified region is known

Given the mean number of successes (μ) that occur in a specified region, we can compute the Poisson probability based on the following formula:

P(x; μ) = (e^-μ) (μ^x) / x!

where x is the actual number of successes that result from the experiment, and e is approximately equal to 2.71828.

Here, Average number of people per 4 minute = 5*4 = 20

To calculate,

P(X>25) = 1 - P(X 25) = 1- 0.88782 = 0.11218   

[ P(X 25) = 0.88782 can be calculated from the Poisson distribution table by looking in the column headed by = 20 and the row headed by X = 25]