Question

The number of cars arriving at a servi-car or bank service window between 3:00 p.m. and 6:00 p.m. on Friday, a Poisson process follows at a rate of 0.25 cars per minute. Calculates the probability that fewer than 4 cars arrive at the bank between 4:00 p.m. and 4:10 p.m. (result at four decimal places)

Answer 1

Given that,

The number of cars arriving at a servi-car or bank service window between 3:00 p.m. and 6:00 p.m. on Friday, a Poisson process follows at a rate of 0.25 cars per minute.

X: Random variable denoting that the number of cars arriving per minute. i.e. X~Poi(0.25)

Now we want to calculate the probability that fewer than 4 cars arrive at the bank between 4:00 p.m. and 4:10 p.m. i.e time interval is 10 minute. Now if X random variable denoting by,

X: Random variable denoting that the number of cars arriving between 4:00 p.m. and 4:10 p.m. i.e. in 10 minute

i.e. X~Poi(10 0.25)

i.e X~ Poi(2.5)

So PMF of X is given by,

where, x = 0, 1, 2,.......

Now our required probability is given by,

  [Round to four decimal places]

Answer:- Probability that fewer than 4 cars arrive at the bank between 4:00 p.m. and 4:10 p.m. is 0.7576 [Round to four decimal places]