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.

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warylucknow warylucknow · Answer 1 · 2020-03-15T11:23:17+01:00

Answer:

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

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:

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

In 60 minutes the number of arrivals is, 33.

In 1 minute the number of arrival will be, [tex]\frac{33}{60}[/tex].

Then in 5 minutes the number of arrivals will be, [tex]\frac{33}{60}\times5[/tex].

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

The number of arrivals in 5 minutes is

[tex]\frac{33}{60}\times5=2.75[/tex]

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