Answer: 0.04769
Step-by-step explanation:
Let the average number of new clients that a sales representative signs in a month be [tex]\lambda[/tex].
Given: [tex]\lambda=22[/tex]
Poisson distribution formula:
[tex]P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex]
The probability that any given sales representative will sign fewer than 15 new clients in a month = P(X<15)
[tex]=\sum^{14}_{x=0}\dfrac{e^{-22}(22)^x}{x!}\approx0.04769\ [\text{By Poisson distribution table}][/tex]
Hence, the probability that any given sales representative will sign fewer than 15 new clients in a month =0.04769
