In a Study of Texting and Driving, 48% of 300 $0.50$

In a study of texting and driving, 48% of 300 adults surveyed said that they text and
drive. Forty-four percent of 300 teens surveyed said that they text and drive. It is
reasonable to regard these samples (adult drivers and teen drivers) as representative of
the corresponding populations. a) Suppose that the true proportion of adults who text and drive is $0.50$ . Show that it is reasonable to approximate the sampling distribution of $\hat { p }$ , the sample proportion of adults who report texting and driving, using a normal distribution.
b) Assuming that half of all adults would report texting and driving, what is the probability of observing a sample proportion of adult texting drivers less than $\hat { p } = 0.48$ in a study with a sample size of 300 ? c) Assuming that half of all teens would report texting and driving, what is the probability of observing a sample proportion of texting teen drivers of greater than $\hat { p } = 0.44$ in a study with a sample size of 300 ?