The number of calls received by call center follows a Poisson process with a rate of 1.5 per minute.What is the probability that a minute goes by without a call?
A)0
B)0.223
C)0.500
D)0.558
E)1

Question

Quizplus · Accepted Answer

The Poisson distribution can be used to model the number of occurrences of a rare event in a fixed amount of time or space. In this case, the rare event is the call, and the distribution is Poisson with a rate of 1.5 calls per minute.

To find the probability that a minute goes by without a call, we can use the Poisson distribution formula:

P(X = 0) = (e^(-λ) * λ^x) / x!

where λ is the rate and x is the number of occurrences (in this case, 0).

Substituting in the values, we get:

P(X = 0) = (e^(-1.5) * 1.5^0) / 0! = e^(-1.5) ≈ 0.223

Therefore, the best choice is B, with a probability of approximately 0.223 that a minute goes by without a call.

The Number of Calls Received by Call Center Follows a Poisson