Suppose that a market researcher wants to estimate the percent of adults in a large city who have cell phones. 500 randomly selected adult residents in this city are surveyed to determine whether they have cell phones.

a)Assume that the true proportion of adults who have cell phones is 0.8. What is the probability that at least 450 of the selected adult residents responded YES? Please briefly explain why you can calculate in this way.

b)Of the 500 people sampled, the researcher found there are 420 who responded YES. Find a 95% confidence interval for the true proportion of adult residents of this city who have cell phones.