Question

During off hours, cars arrive at a tollbooth on the East-West toll road at an average rate of 0.6 cars per minute. The arrivals are distributed according to a Poisson distribution.

What is the probability that during the next minute, three cars will arrive?

What is the probability that during the next five minutes, three cars will arrive?

What is the probability that during the next five minutes, three or less cars will arrive?

IS THERE A WAY TO SHOW WORK IN EXCEL?

Answer 1

Let X is a random variable shows the number of cars arrive in a minute. Here X has Poisson distribution with parameter $\lambda=0.6$ .

The probability that during the next minute, three cars will arrive is

$P(X=3)=\frac{e^{-0.6}0.6^{3}}{3!}=0.01976$

Excel function used: "=POISSON(3,0.6,FALSE)"

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Let X is a random variable shows the number of cars arrive in five minutes. Here X has Poisson distribution with parameter $\lambda=5\cdot 0.6=3$ .

The probability that during the next five minute, three cars will arrive is

$P(X=3)=\frac{e^{-3}3^{3}}{3!}=0.22404$

Excel function used: "=POISSON(3,3,FALSE)"

The probability that during the next five minutes, three or less cars will arrive is

$P(X\leq 3)=\sum_{x=0}^{3}\frac{e^{-3}3^{x}}{x!}=0.64723$

Excel function used: "=POISSON(3,3,TRUE)"