Solve the following:
Q: A very large number of fish are swimming in a lake. Their weights are normally distributed with mean 1.30kg and a standard deviation 0.40kg. Fish caught with weights less than 0.5kg have to be thrown back.
a) If an angler catches a randomly selected fish, what is the probability that the fish has to be thrown back?
b) find the probability that it is not thrown back and, at the same time, does not exceed the record 2.06kg.
c) The local angling club decides at the beginning of the season to give prizes for any fish caught in the heaviest 5% of the fish pop. What should be the minimum weight of a fish to warrant a prize?