On a Certain Athletics Team, Athletes Get a $250 Bonus $$f ( x ) = \left\{ \begin{array} { l l } \frac { x ^ { 2 } } { 140 } & x = 0,1 , \ldots , 22 \\0 & \text { else. }\end{array} \right.$$

Short Answer

On a certain athletics team, athletes get a $250 bonus if they run their one-mile race in under 4 minutes. If they do not, they pay the club $10. There are 7 athletes on the team. The number of athletes who run their mile in under 4 minutes has the probability mass function. $$f ( x ) = \left\{ \begin{array} { l l } \frac { x ^ { 2 } } { 140 } & x = 0,1 , \ldots , 22 \\0 & \text { else. }\end{array} \right.$$ The bonuses are withdrawn from and the fines are charged to the team's account. After all the athletes have run their mile, what is the expected value of the change in the balance of the team's account?