Answer
$\overline{T}=25^{\circ} F$ and $n=4$
Work Step by Step
Consider the average value of temperature as follows: $\overline{T}=\dfrac{1}{360-0} \int_0^{365} [37 \sin (\dfrac{2 \pi}{365})(x-101))+25] dx$
Applying Simpson's Rule, now we will plug in the above equation $a=0; b=365$
Suppose that $n=4$
So, we get $\overline{T}=25^{\circ} F$. This means that for this average value of temperature, the value of $n=4$ is sufficient.
So, $\overline{T}=25^{\circ} F$ and $n=4$
