On weekdays from 11: 30 am to 2:00 pm customers arrive at a hotdog street vendor at the rate of 25 per 30 minute interval. Assume that this process can be well modeled by
The Poisson distribution. What is the probability that the vendor will have to wait at least
3 minutes for a customer?
A) 0.9179
B) 0.6734
C) 0.0821
D) 0.3912
E) 0.8854

Question

Quizplus · Accepted Answer

The rate of customers arriving per minute can be calculated as:
25 customers / (30 minutes * 2) = 0.4167 customers per minute
Let X be the time (in minutes) the vendor has to wait for a customer to arrive. X follows an Exponential Distribution with parameter λ = 0.4167:
P(X ≥ 3) = e^(-λ * 3) = e^(-0.4167 * 3) = 0.0821
Therefore, the probability that the vendor will have to wait at least 3 minutes for a customer is 0.0821. The correct answer is choice C.

On Weekdays from 11: 30 Am to 2:00 Pm Customers