Compute Probabilities of a Poisson Random Variable
-A help desk receives an average of four calls per hour on its toll-free number. For any given hour, find the probability that it will receive exactly seven calls. Use the Poisson distribution.
A) 0.0596
B) 0.0030
C) 522.0448
D) 0.0087

Question

Quizplus · Accepted Answer

The probability of receiving exactly seven calls in an hour, given an average rate ($\lambda$) of 4 calls per hour, can be calculated using the Poisson distribution formula: $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$. Substituting $\lambda = 4$ and $k = 7$, we get $P(X=7) = \frac{e^{-4} 4^7}{7!}$, which calculates to approximately 0.0596.