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Shower temperature at the Spokane Club showers is regulated automatically. The heater kicks in when the...

Shower temperature at the Spokane Club showers is regulated automatically. The heater kicks in when the temperature falls to 970F and shuts off when the temperature reaches 1070 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(97,107).
Find the mean temperature.
Find the standard deviation of the temperature.
Find the probability that the temperature is between 990 and 1010.
Find the 75th percentile for water temperature.

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