The assignment is given:
In a heat regulated room, we have two temperature limits $T_{\text{min}} = 16$ and $T_{\text{max}} = 24$. If the temperature is between $T_{\text{min}}$ and $T_{\text{max}}$, the temperature regulation system is off.
Let's assume that if there was no heat regulation in the room, the temperature would be normal distributed, with then mean value $\mu = 21$ (Celsius) and the standard deviation $\sigma = 2.7$.
1) How much percentage of time, is the heat regulation system off?
Let's assume that the room air circulation is improved, so that the temperature regulation system now if off $92\%$ of time, with the same values, $\mu$, $T_{\text{min}}$ and $T_{\text{min}}$ as in (1).
2) What is the standard deviation ($\sigma$) now?
Using R, I have found that the heat regulation is off about $16.2\%$ of the time, using the following command.
1 - pnorm(24,21,2.7) - pnorm(16,21,2.7)
This is correct, I know.
However, in the latter problem, I quickly ran into problems. I asked my professor, and he could not figure it out either.
Anyone here, willing to help me out?