Outpatient clinics are hospital clinics that have appointments for patients who visit the hospital without being admitted. These are quite similar to your local General Practitioner's (GP's) office. Outpatient clinics at one local hospital include Urology, Spasticity Management, Sex & Fertility, Upper Limb Clinic, Plastic Surgery and Adult spina bifida. At one particular clinic, it is known that the distribution of appointment times (in minutes) looks like f(t) = at2 + bt where 0 t 10. Hospital administrative staff do not know the values of a and b. They do know that the average appointment duration is 5 minutes.