Because of safety considerations, in May 2003 the Federal Aviation Administration (FAA) changed its guidelines for how small commuter airlines must estimate passenger weights. Under the old rule, airlines used180 poundsas a typical passenger weight (including carry-on luggage) in warm months and 185 pounds as a typical weight in cold months.A journal reported that an airline conducted a study to estimate average passenger plus carry-on weights. They found an average summer weight of183 poundsand a winter average of190 pounds.Suppose that each of these estimates was based on a random sample of100 passengersand that the sample standard deviations were16poundsfor the summer weights and24poundsfor the winter weights.(a)Construct a 95% confidence interval for the mean summer weight (including carry-on luggage) of this airline's passengers. (Use technology to calculate the critical value. Round your answers to three decimal places.)

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Interpret a 95% confidence interval for the mean summer weight (including carry-on luggage) of this airline's passengers.There is a 95% chance that the true mean summer weight (including carry-on luggage) of this airline's passengers is between these two values.We are 95% confident that the true mean summer weight (including carry-on luggage) of this airline's passengers is directly in the middle of these two values. There is a 95% chance that the true mean summer weight (including carry-on luggage) of this airline's passengers is directly in the middle of these two values.There is a 95% chance that the true mean summer weight (including carry-on luggage) of this airline's passengers is one of these two values.We are 95% confident that the true mean summer weight (including carry-on luggage) of this airline's passengers is between these two values.(b)Construct a 95% confidence interval for the mean winter weight (including carry-on luggage) of this airline's passengers. (Use technology to calculate the critical value. Round your answers to three decimal places.)

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Interpret a 95% confidence interval for the mean winter weight (including carry-on luggage) of this airline's passengers.We are 95% confident that the true mean winter weight (including carry-on luggage) of this airline's passengers is directly in the middle of these two values.There is a 95% chance that the true mean winter weight (including carry-on luggage) of this airline's passengers is directly in the middle of these two values. There is a 95% chance that the true mean winter weight (including carry-on luggage) of this airline's passengers is one of these two values.We are 95% confident that the true mean winter weight (including carry-on luggage) of this airline's passengers is between these two values.There is a 95% chance that the true mean winter weight (including carry-on luggage) of this airline's passengers is between these two values.(c)The new FAA recommendations are190 poundsfor summer and195 poundsfor winter. Comment on these recommendations in light of the confidence interval estimates frompart (a)andpart (b).These new FAA recommendations don't seem accurate, since neither recommendation value is contained within its respective 95% confidence interval.Only the new winter FAA recommendation seems accurate, since only the new winter recommendation value is contained within its 95% confidence interval. These new FAA recommendations seem accurate, since both recommendation values are contained within their respective 95% confidence interval.Only the new summer FAA recommendation seems accurate, since only the new summer recommendation value is contained within its 95% confidence interval.