Question

the number of cars arriving at a bank car service between 3:00 pm and 6:00 pm on Friday, according to a Poisson process at the rate of 0.3 cars per minute. Calculate the probability that at least 4 cars arrive at the bank between 4:00 pm and 4:10 pm

Answer 1

Answer:-

Given that:-
The number of cars arriving at a bank car service between 3:00 pm and 6:00 pm on Friday, according to a Poisson process at the rate of 0.3 cars per minute. Calculate the probability that at least 4 cars arrive at the bank between 4:00 pm and 4:10 pm

The number of cars arriving at a bank car service between 3:00 pm and 6:00 pm on Friday, according to a Poisson process at the rate of 0.3 cars per minute.

X: Random variable denoting that the number of cars arriving per minute .i.e.

Now we want to calculate the probability that fewer than 4 cars arrive at the bank between 4:00pm and 4:10 0.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

  

So PMF of X is given by,

where ,

Now our required probability is given by,

The probability that at least 4 cars arrive at the bank between 4:00 pm and 4:10 pm is 0.6472