Customers arrive randomly and independently at a service window, and the time between arrivals has an exponential distribution with a mean of 12 minutes. Let X equal the number of arrivals per hour. What is P (X=10) ?

0.018133

Step-by-step explanation:

Given that customers arrive randomly and independently at a service window, and the time between arrivals has an exponential distribution with a mean of 12 minutes.

Let X equal the number of arrivals per hour.

X is having average as reciprocal of 12 minutes

i. e. in one hour on an average expected customers to arrive is 60/12 = 5

X being reciprocal of exponential is Poisson with parameter = 5

Probability that 10 customers arrive in one hour

=P (X=10)

=0.018133