At the Fidelity Credit Union, a mean of 6.7 customers arrive hourly at the drive through window. What is the probability that, in any hour, no more than 3 customers will arrive? ( Round your answer to 4 decimal places) O A. 0.0617 O B. 0.9012 O C. 0.5 O D. 0.0371 O E. 0.0988 

When an event occurs at a fixed rate, it is best modeled by the poison probability distribution.

Mathematically, we have that

P(x = r) = e^-u * u^r/r!

u is the fixed rate at which the event is occurring.

In the case of ours, u is 6.7

We are to find P(x ≤ 3)

P(x ≤ 3) = P(x = 3) + P(x = 2) + P(x = 1) + P(x = 0)

At x = 3

P(x = 3) = e^-6.7 * 6.7^3/3!

P(x = 3) = 0.3702/6

P(x = 3) = 0.0617

At x = 2

P(x = 2) = e^-6.7 * 6.7^2/2!

P(x = 2) = 0.0553/2

P(x = 2) = 0.0276

At x = 1

P(x = 1) = e^-6.7 * 6.7^1/1!

P(x = 1) = 0.0083/1

P(x = 1) = 0.0083

At x = 0

P(x = 0) = e^-6.7 * 6.7^0/0!

P(x = 0) = 0.0012/1

P(x = 0) = 0.0012

P(x ≤ 3) = 0.0617+0.0276+0.0083+0.0012 = 0.0988

Option D