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:

$P(X=4) = 0.164125$

Step-by-step 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:

$P(X=4) = \frac{5.3^4 * e^{-5.3}}{4!}$

$P(X=4) = \frac{789.0481 * 0.004992}{4*3*2*1}$

$P(X=4) = \frac{3.939}{24}$

$P(X=4) = 0.164125$

Hence, the probability of exactly 4 complaints is 0.164125 .