Problem 3. Cargo Load (3 pts} An overloaded aircraft may not be able to leave the ground, or if it does become airborne, it may exhibit unexpected and unusually poor flight characteristics. If not properly loaded, the initial indication of poor performance usually takes place during takeoff [2]. Therefore, Compliance with the weight and balance limits of any aircraft is critical to flight safety. The Airbus A330 is a medium- to long-range wide-body twin-engine Jet airliner made by Airbus. In general, this aircraft can carry 2'0 tons (154,000 pounds] of cargo. Out ofthis 2'0 tons, MD Airways specified the Total Luggage Weight limit to be less than 10 tons (22046 pounds). a} Use the sampled data to estimate the average luggage weight for each passenger. a. Define the RV and find its mean [E(X]] also find standard deviation (sigma). b) Assume that the expected value and standard deviation calculated in part (al are the true population mean and standard deviation of luggage weight for each passenger. What is the probability that combinedgross weight of all passengers' luggage (total luggage weight} to be more than Total Luggage Weight limit of the MD Airways? Interpret your results P (Z X,- s 22,046) :1? Hint: There is no sampling distribution for EXE, but you can easily convert it to I? , and then find the probability of 2?. c] Draw a histogram of the luggage's weight. Assume the average weight for each checked-in luggage is 50 lbs., what is the max number of luggage being checked in by ONE passenger. d) Try to construct a PMF table for the Number of lCheck-in luggage by each passenger