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The weight of any passenger using a ferry service has a normal distribution with mean 168 pounds and standard deviation 19 pounds. A particular ferry carries 25 passengers. Safety regulations state that for this particular ferry, the total weight of passengers on the boat should not exceed 4,250 pounds more than 5% of the time.
a) Find the probability that the total weight of passengers on the ferry will exceed 4,250 pounds.
b) Find the 95th percentile of the distribution of the total weight of passengers on the ferry.
c) Is the ferry complying with safety regulations? Explain reasoning.
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