Question

Let average number of customers arriving at a bank is 40/hour. Find the probability that exactly 6 customers will arrive at the bank during a 15 minute period.

Answer 1

Given:

Let average number of customers arriving at a bank is 40/hour.

To find : The probability that exactly 6 customers will arrive at the bank during a 15 minute periodb:

Now,

Mean = = 40*15/60 = 10

Let X be customer's arrival time at the bank .

X ~ Poisson (=10)

The probability density function of Poisson distribution is given by

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

P(X=6) = e^-10 * (10)^6 /6!

= 0.0631

P(X=6) = 0.0631

Therefore the probability that exactly 6 customers will arrive at the bank during a 15 minute period is 0.0631