Customers arrive at a movie theatre at the advertised movie time only to find that they have to sit through several previews and pre preview ads before the movie starts. Many complain that the time devoted to previews is also long (The Wall Street Journal, October 12, 2012). A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was four minutes. Use that as a planning value for the standard deviation in answering the following questions.
a. If we want to estimate the population mean time for previews at movie theatres with a margin of error of 75 seconds, what sample size must be used? Suppose 95% confidence.