Another Probability Problem: A company establishes a fund of $120 from which it wants

[Steven G]

A company establishes a fund of $120 from which it wants to pay an amount, $C, to any of its 20 employees who achieve a high performance level during the coming year. Each employee has a 2% chance of achieving a high performance level during the coming year, independent of any other employee. Determine the maximum value of C for which the probability is less than 1% that the fund will be inadequate to cover all payments for high performance.


I was given the solution.

Let X denote the number of employees that achieve the high performance level. Then X follows a binomial distribution with parameters n = 20 and p= 0.02. We want to We want to determine x such that Pr(X>x)<=0.01 or .99<Pr(X<=x)....

I am confused as to how C is not part of this binomial distribution. That is why is C max when Pr(X<x)>=.99? I see clearly that to max C we want x to be as small as possible