Answer
$\overline{T}=25^{\circ} F$; $n=4$
Work Step by Step
The average value of the temperature is given as follows:
$\overline{T}=\dfrac{1}{360-0} \int_0^{365} [37 \sin (\dfrac{2 \pi}{365})(x-101))+25] dx ....(1)$
Now, by using Simpson's Rule, we need to plug into equation (1), $a=0; b=365; $ and let us suppose that $n=4$
Thus, we have $\overline{T}=25^{\circ} F$; this implies that for this average value of temperature, the value of $n=4$ is sufficient.
