An orthodontist has three financing packages, and each has a different service charge. He estimates that 30% of patients use the first plan, which has a $10 finance charge; 50% use the second plan, which has a $2 0 finance charge; and 20% use the third plan, which has a $30 finance charge.
a) Find the expected value of the service charge.
b) Find the standard deviation of the service charge.