Question

The Quick Snap photo machine at the Lemon County bus station takes snapshots in exactly 80 seconds. Customers arrive at the machine according to a Poisson distribution at the mean rate of 15 per hour. On the basis of this information, determine the following: (Provide formulas)

a.	the average number of customers waiting to use the photo machine
b.	the average time a customer spends in the system
c.	the probability an arriving customer must wait for service.

Answer 1

Solution :

Given that ,

mean = $\mu$ = 15

x = 80

Using Poisson probability formula,

P(X = x) = (e^{- $\mu$} * $\mu$ ^x ) / x!

P(X = 80 ) = (e^-15 * 15⁸⁰⁾ / 80! =

Probability = 0

Option a ) is correct.