A survey of adults in the United States found that 61% ate at a restaurant at least once in the past week. You randomly select 30 adults and ask them whether they ate at a restaurant at least once in the past week.

(a) Verify that a normal distribution can be used to approximate the binomial distribution.

(b) Find the probability that at most 14 adults ate at a restaurant at least once in the past week.

(c) Is it unusual for exactly 14 out of 30 adults to have eaten in a restaurant at least once in the past week? Explain your reasoning.