## Related questions with answers

Shower temperature at the Oxnard Health Club showers is regulated automatically. The heater kicks in when the temperature falls to $99^{\circ} \mathrm{F}$, and shuts off when the temperature reaches $107^{\circ} \mathrm{F}$. 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 75 th percentile for water temperature.

Solution

Verifieda) In this task, we need to find the mean temperature. The given is that the shower temperature is regulated automatically, the heaters turn on when the temperature falls to $99\degree$F and turn off when the temperature reaches $107\degree$F. At that moment, the water temperature is a uniformly distributed random variable $\mathcal{U\qty(99,107)}$.

So, we need to find $\mu$ of this distribution.

What is the mean of this distribution?

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