Shower temperature at the Oxnard Health Club showers is regulated automatically. The heater kicks in when the temperature falls to 998F and shuts off when the temperature reaches 1078F. Water temperature then falls slowly until the heater kicks in again. At a given moment, the water temperature is a uniformly distributed random variable U(99,107).
(a) Find the mean temperature.
(b) Find the standard deviation of the temperature.
(c) Find the 75th percentile for water temperature.