Question

The mean number of customers arriving at a restaurant during a 15-minute period is 8. Find the probability that at least 4 customers will arrive at the restaurant during a 15-minute period.

Answer 1

Given :

The mean number of customers arriving at a restaurant during a 15-minute period is 8.

Mean = $\lambda$ = 8

Let X be the number of customers will arrive at the restaurant during a 15-minute period.

X follows the Poisson distribution with parameter $\lambda$ = 8.

X ~ Poisson ($\lambda$=8)

The probability density function of Poisson distribution is given by

P(X=x) = e^-$\lambda$ * $\lambda$ ^x /X!

The probability that at least 4 customers will arrive at the restaurant during a 15-minute period :

P(X$\geq$4) = 1 - P(X < 4)

= 1 - $\sum_{X=0}^{3}$ e^-8 * 8^x /X!

= 1 - 0.0424

= 0.9576

Therefore the probability that at least 4 customers will arrive at the restaurant during a 15-minute period is 0.9576