Problem 5. When fishing off the shores of Florida, a spotted sea trout must be between 14 and 24 inc

Problem 5. When fishing off the shores of Florida, a spotted sea trout must be between 14 and 24 inches long before it can be kept; otherwise, it must be returned to the waters. In a region of the Gulf of Mexico, the lengths of spotted sea trout that are caught are normally distributed with a mean of 22 inches and a standard deviation of 4 inches. Assume that each spotted trout is equally likely to be caught by a fisherman. The fisherman could be a poacher. Let X be the length of the trout.(a) What is the probability that a fisherman catches a spotted sea trout within the legal limits?(b) The fisherman caught a spotted sea trout. He wants to know whether the length is in the top 5% of the length of spotted sea trout in that region. Find the length X for which only 5% of the spotted sea trout in this region will be larger than X.(c) What is the probability that the fisherman will catch three trout outside the legal limits before catching the first legal spotted sea trout (between 14 and 24 inches).(d) A fisherman has the following revenue function: Y = 1+2X where Y is the amount of dollars he makes for selling trouts. Compute the expected revenue, the variability of that revenue and the probability that revenue will be larger than $67.