Question

0.8 points S Suppose that the average number of new clients that a sales representative signs in a month is 25 and that the distribution of this random variable is Poisson. What is the probability that any given sales representative will sign more than 30 new clients in a month? Answer to at least four decimal places. You may find it easier to use excel than to use a calculator for this one

Answer 1

Let X be the number of new clients that a sales representative signs in a month

and the average number of new clients that a sales representative signs in a month is 25

X ~ P(25)

$P(X> 30) =1-P(X\leq 30) =1-\sum_{x=0}^{30}\frac{e^{-25}25^{x}}{x!}=1-0.8633=0.1367$

Answer: 0.1367