#### Answer

See graph, $56^\circ F$, July.

#### Work Step by Step

Based on the given function $y=16sin(\frac{\pi}{6}-\frac{2\pi}{3})+40$, we can calculate the values for each month as shown in the table, and then graph the function as shown in the figure. It can be seen that the highest average monthly temperature happens in July with a value of about $56^\circ F$.