Mathematics: Suppose that the average number of new clients that a sales representative signs in a month is 22 and that the distribution of this random variable is Poisson. What is the probability that any given sales representative will sign fewer than 15 new clients in a month

Suppose that the average number of new clients

stranger123

07.02.2022

0.04769

Step-by-step explanation:

Let the average number of new clients that a sales representative signs in a month be $\lambda$ .

Given: $\lambda=22$

Poisson distribution formula:

$P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}$

The probability that any given sales representative will sign fewer than 15 new clients in a month = P(X<15)

$=\sum^{14}_{x=0}\dfrac{e^{-22}(22)^x}{x!}\approx0.04769\ [\text{By Poisson distribution table}]$

Hence, the probability that any given sales representative will sign fewer than 15 new clients in a month =0.04769

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kynlie1760

07.03.2021

Step-by-step explanation:

not wrong that is super right

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