I'm stuck with the following probability problem:
The lifetime of a lamp in hours was modeled by the random variable $X$ which has the following probability distribution:
$$\begin{array}{c|c|c|c} X& 5 & 6 & 7 & 8 & 9 & 10\\ \hline p_i & 0.1 & 0.1 & 0.2 & 0.4 & 0.1 & 0.1 \end{array}$$
Each lamp costs $\$10$ dollars to be manafactured. If the lifespan of the lam is inferior to $6$ hours the vendor will make up for the buyer with a $\$15$ dollars.
What should it be the selling price of each lamp for the vendor go get an average of $\$20$ dollars by lamp?
Can anyone help me?
I assume the problem boils down to expectancy.