Question

The arrival of customers over fixed time intervals in a bank follow a poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrival is between 1 and 3 minutes is _______ (correct to two decimal places).

Answer 1

Answer:

P(1 ≤ x ≤3) = 0.2906

Step-by-step explanation:

Arrival rate is 30 customers per hour.

60 minutes = 30 customers

1 minute = 30/60 = 1/2 customers

\lambda  = 1/2

For poisson distribution formula is;

p(x=X) = $\frac{e^{-\lambda}\lambda^{x}}{x!}$

P(1 ≤ x ≤3) = P(x≤3) - P(x≤1)

                = [1 - P(x=3)] - [1-P(x=1)]

                 = $\frac{-e^{-1/2}}{48}$+$\frac{e^{-1/2}}{2}$

                  = e^{-0.5}[$\frac{23}{48}$

                  = 0.2906