At Mike's Auto Service, the mean time to diagnose a problem is 30 minutes with a standard deviation of 8 minutes. The mean time to perform the repairs once the diagnosis is complete is 180 minutes with a standard deviation of 45 minutes.
a) Find the mean and standard deviation of the total time to complete an auto repair.
b) If Mike charges $40 per hour for diagnosis and $120 per hour for repair, find the mean total cost and the standard deviation of the total cost.