An SRS of 400 American adults is asked, “What do you think is the most serious problem facing our schools?”

Suppose that in fact 40% of all adults would answer “violence” if asked this question. The proportion ^p of the sample who answer “violence” will vary in repeated sampling. In fact, we can assign probabilities to values of ^p using the Normal density curve with mean 0.4 and standard deviation 0.024.

Use this density curve to find the probabilities of the event:

(b) Less than 35% of the sample believes that violence is the most serious problem.