Question

What is the probability that exactly 10 customers will arrive in 1 hour, when the mean arrival rate is 15 customers per hour, and interarrival times are exponentially distributed?

a. 0.0486
b. 0.1185
c. 0.0699
d. 0.9301
e. 0.8815

Answer 1

a. 0.0486

Explanation:

Given that the mean arrival rate is 15 customers per hour, and interarrival times are exponentially distributed

When the interarrival times are exponential, no of customers arriving per hour is Poisson with mean = 15

The probability that exactly 10 customers will arrive in 1 hour

`=P(x=10)` where X is a Poisson random variable with mean = 15

`=e^(-15)((15^(10) )/(10!))\\  = 0.04861`

Thus we find that probability is 0.04861 and round it off to 4 decimals

Prob = 0.0486

Hence option a is right