The time required for an automotive center to complete oil change service on an automobile approximately follows a normal? distribution with a mean of 19 minutes and a standard deviation of 3.6 minutes.

a)  The automotive center guarantees customers that the service will take no longer than 20.5 minutes. If it does take? longer, the customer will receive the service for? half-price. What percent of customers receive the service for? half-price?

I started the equation but do not know the last part- P (X>20.5)= P(z>(20.5-19)/3.6)= P (z>0.4167)= 1- P (z<= 0.4167)=1- (jQuery200045582368902509196_1502813432629?)

b)  If the automotive center does not want to give the discount to more than 9?% of their? customers, how long should it make the guaranteed time limit?  Which percentile have you just found?