Because of safety considerations, in May 2021 the Federal Aviation Administration (FAA) changed its guide- lines for how small commuter airlines must estimate passenger weights. Under the old rule, airlines used 160 pounds as a typical passenger weight (including carry-on luggage) in warm months. A journal reported that an airline con- ducted a study to estimate average passenger plus carry-on weights. They found an average summer weight of 10aß pounds. Suppose that each of these estimates was based on a random sample of 100 passengers and that the sample standard deviations were 15 pounds for the summer weights. Construct a 95% confidence interval for the mean summer weight (including carry-on luggage) of this airline's pas- sengers. (Show the detailed steps, and round your answer to three decimal places.)
