Question

The average number of customers arriving at a gas station is 33 per hour during lunch hours. Use equation to denote the number of arrivals in a 5 minute time interval. Assume the customers arrive independently and the number of arrivals within each 5 minutes follows a Poisson distribution. Keep at least 4 decimal digits if the result has more decimal digits.

Answer 1

Answer:

The equation denoting the number of arrivals in 5 minutes is, $\frac{33}{60}\times5$.

The number of arrivals in 5 minutes is 2.75.

Step-by-step explanation:

Let X = number of customers arriving at a gas station in an hour.

The average customers arriving at a gas station in an hour is, λ = 33.

The random variable X follows a Poisson distribution with parameter λ.

The probability mass function of a Poisson distribution is:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0,1,2,3...$

In 60 minutes the number of arrivals is, 33.

In 1 minute the number of arrival will be, $\frac{33}{60}$.

Then in 5 minutes the number of arrivals will be, $\frac{33}{60}\times5$.

The equation denoting the number of arrivals in 5 minutes is, $\frac{33}{60}\times5$.

The number of arrivals in 5 minutes is

$\frac{33}{60}\times5=2.75$

Thus, the number of arrivals in 5 minutes is 2.75.