Answer: 0.04769
Explanation:
Let the average number of new clients that a sales representative signs in a month be
.
Given:

Poisson distribution formula:

The probability that any given sales representative will sign fewer than 15 new clients in a month = P(X<15)
![=\sum^(14)_(x=0)(e^(-22)(22)^x)/(x!)\approx0.04769\ [\text{By Poisson distribution table}]](https://img.qammunity.org/2021/formulas/mathematics/college/ufyg9bsbo5a5ar5s5mihfztzrqbvz6l9ds.png)
Hence, the probability that any given sales representative will sign fewer than 15 new clients in a month =0.04769