Suppose you are a financial consultant trying to determine whether a group of 1,500 country club members represents a good source of potential clients for a real estate firm in New Jersey. To determine the potential business, you decide to analyze the size of the club members’ purchases of homes. A random sample of 90 members produces a sample mean of $280,000 with a sample standard deviation of $75,000. Using this information, construct a 95 % confidence interval for the mean purchases N = 1,500, n = 90, X̅ = $280,000, and s = $75,000.