Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.If X = the number of arrivals per minute,find the probability of 3 customers arriving within a minute.
A)1.00
B).1494
C).224
D).3734

Question

Quizplus · Accepted Answer

The Poisson distribution formula is:

P(X = k) = (e^(-λ) * λ^k)/k!

Where:
λ = the average number of arrivals/events in the given time period
k = the number of arrivals/events we're interested in finding the probability of

In this case, we know that λ = 3 (3 customers per minute), and we want to find the probability of 3 customers arriving in a minute, so k = 3.

Substituting these values into the formula, we get:

P(X = 3) = (e^(-3) * 3^3)/3! = 0.224

So the probability of 3 customers arriving in a minute is 0.224, or approximately 0.22. Therefore, the best choice is C.

Consider a Poisson Distribution with an Average of 3 Customers