Assume that customer arrivals at a small cafe can be modeled by a Poisson distribution. The average arrival rate is 3 customers per hour. What is the probability of exactly 2 arrivals in the next hour (to two decimal places)?
A) 1.00
B) 0.15
C) 0.22
D) 0.45

Question

Quizplus · Accepted Answer

The probability of exactly 2 arrivals in the next hour can be calculated using the Poisson probability formula:
P(X = 2) = (e^-λ * λ^X) / X!, where X is the number of arrivals, λ is the average arrival rate, and e is the mathematical constant approximately equal to 2.71828.

Substituting λ = 3 and X = 2, we get:
P(X = 2) = (e^-3 * 3^2) / 2!
P(X = 2) = (0.0498 * 9) / 2
P(X = 2) = 0.2241 or 0.22 (rounded to two decimal places)

Therefore, the best choice is C, with a probability of 0.22.

Assume That Customer Arrivals at a Small Cafe Can Be