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An airline operates a baggage weight allowance of 25 kg per passenger. Check-in records show that the weight X (in kg) of a passenger's baggage can reasonably be assumed to be Normally distributed with mean 24 kg and standard deviation 1 kg. A passenger with baggage weighing more than 25 kg is charged $5 for each kg by which the weight of his or her baggage exceeds 25 kg, all fractions of a kg being rounded up to the next whole number. Let Y be the excess baggage charge in $ for a randomly chosen passenger. (a) (6 points) Find the probabilities P(Y = 0), P(Y = 5), P(Y = 10) and P(Y =15). (b) (3 points) Suppose P(Y > 15) is too small and negligible, nd the mean and variance of Y. (c) (5 points) Assuming that 100,000 passengers independently y with this airline in a year. Let T be the total excess baggage costs paid to this airline in a year. Find the mean and variance of T. Suppose P(T>k)=0.05, nd the value of k