Question

The number of cars arriving at a gas station can be modelled by Poisson distribution with the average rate of 5 cars per 10 minutes. a. The probability that one car will arrive to a gas station in a 5 -minute interval is _________ b. The probability that at least one car will arrive to the gas station in a 10 - minute interval is ______

Answer 1

X ~ Poi ( )

Where = 5 cars per 10 min

Poisson probability distribution is

P(X) = e^- * ^X / X!

a)

For 5 min, = 5 * 5 / 10 = 2.5

P(X = 1) = e^-2.5 * 2.5 = 0.2052

b)

For 10 minutes, = 5

P(X >= 1) = 1 - P(X = 0)

= 1 - e^-5

= 0.9933