Question

Sports Scores Hot Line receives, on the average, 8 calls per hour requesting the latest sports scores. The distribution is Poisson in nature. For any randomly selected hour, find the probability that the company will receive a. At least 8 calls P(at least)

Answer 1

0.54704 is the probability that the company will receive atleast 8 calls.

Explanation:

We are given the following information in the question:

Mean number of calls = 8 calls per hour

`\lambda=8`

The distribution of calls Hot Line receives can be treated as a Poisson distribution.

We have to find the probability that the company will receive at least 8 calls

Formula:

`P(X =k) = \displaystyle(\lambda^k e^(-\lambda))/(k!)\\\\ \lambda \text{ is the mean of the distribution}`

P(atleast 8) =

`P( x \geq 8) =1 - P(x < 8)\\\\=1 - \displaystyle\sum_(x=0)^(x=7) \displaystyle(\lambda^x e^(-\lambda))/(x!)\\\\ =1-0.45296\\\\= 0.54704`

Thus, 0.54704 is the probability that the company will receive atleast 8 calls.