Question

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals. The probability of 5 cars arriving over a five-minute interval is __________ .

Group of answer choices

0.0940

0.0417

0.1500

0.1008

0.2890

Answer 1

Solution: Let x be the number of cars arriving over five minutes of an interval. We are given that a random variable x follows the Poisson distribution with a mean of 3 cars. Therefore, we have:

X ~ Poisson (1= 3)

We are required to find the probability of 5 cars arriving over a five-minute interval.

PGC 5)_e3 PT = 5) = 6 0.049787068 x 243 = = 0.1008 120

Therefore, the correct option is 0.1008