A Dentist Has Found That a Certain Procedure Has a Cost

Essay

A dentist has found that a certain procedure has a cost (in thousands of dollars) with probability density function: $$f ( x ) = \left\{ \begin{array} { l l } 2 e ^ { - 2 t } & x \geq 0 \\0 & \text { else }\end{array} \right.$$ . The dentist also found that if she charges the patients 10% of the cost up front, then k, the amount of money the insurance company pays, only in 12% of the time exceeds the remaining cost. Find k.