Question

The number of cars that arrive at a bank’s drive-through window between 4:00 pm and 7:00 pm on a Friday follows a Poisson process at the rate of 0.42 car every minute. Compute the probability that the number of cars that arrive at the bank between 5:25 pm and 5:35 pm is at most 5 cars.

Answer 1

Ans:

Time interval between 5:25 pm and 5:35 pm is 10 minutes.

Average number of cars in 10 minutes=0.42*10=4.2 cars

P(x=k)=exp(-4.2)*(4.2^k/k!)

P(atmost 5 cars)=P(x<=5)

=exp(-4.2)*(4.20/0!+4.21/1!+4.22/2!+4.23/3!+4.24/4!+4.25/5!)

=0.7531