The Principal at George Washington High School Has Been Asked $n = 40$

The principal at George Washington High School has been asked to estimate the proportion of students at the school who drive to school and use the school parking lot. He takes a random sample of size $n = 40$ students and calculates a sample proportion, $\hat { p } = 0.8$ . "Now," he exclaims, "since my sample size is pretty large, the sampling distribution of the sample proportion is approximately normal." Write a short paragraph that explains why his statement is not correct.