Question

A restaurant gets an average of 5.3 complaints per day from its patrons. Use the Poisson distribution formula to find the probability that on a given day the restaurant will receive

Answer 1

Question: A restaurant gets an average of 5.3 complaints per day from its patrons. Use the Poisson distribution formula to find the probability that on a given day the restaurant will receive exactly 4 complaints

Answer:

`P(X=4) = 0.164125`

Explanation:

Given

`\bar{x} = 5.3` -- average

Required

Determine the probability of receiving 4 complaints in a day

Since, it follows a poisson distribution, the probability is calculated as:

`P(X=x) = \frac{\bar{x}^x * e^{-\bar{x}}}{x!}`

In this case:

`x = 4`

So, we have:

`P(X=4) = (5.3^4 * e^(-5.3))/(4!)`

`P(X=4) = (789.0481 * 0.004992)/(4*3*2*1)`

`P(X=4) = (3.939)/(24)`

`P(X=4) = 0.164125`

Hence, the probability of exactly 4 complaints is 0.164125 .