THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Suppose you know that the number of complaints coming into a phone center averages 4.2 every ten minutes.Assume that the number of calls follows the Poisson distribution.
-What is the probability that there are three or fewer calls during the next ten minutes?
A)0.211
B)0.372
C)0.396
D)0.425

Question

Quizplus · Accepted Answer

We are given λ (average number of complaints per ten minutes) which is 4.2.
We know that the Poisson distribution applies to the number of complaints, so we can use the Poisson formula:
P(X ≤ 3) = e^(-λ) * (λ^0/0!) + e^(-λ) * (λ^1/1!) + e^(-λ) * (λ^2/2!) + e^(-λ) * (λ^3/3!)
P(X ≤ 3) = e^(-4.2) * (4.2^0/0!) + e^(-4.2) * (4.2^1/1!) + e^(-4.2) * (4.2^2/2!) + e^(-4.2) * (4.2^3/3!)
P(X ≤ 3) = 0.396
Therefore, the probability that there are three or fewer calls during the next ten minutes is 0.396.