Young cod are transferred from a hatchery to sea cages, and it then takes an average of 26 months for cod to reach market size, with a standard deviation of one month. The average weight of market-size cod is 3.75 kilograms with a standard deviation of 0.38 kilograms, and we’ll assume that it’s Normally distributed. You have developed a new feeding program for cod in sea cages, and your first sample of 52 cod has reached market size in an average of 25.6 months and weighs an average of 3.9 kilograms.

a) What is the probability of a random sample of 52 cod reaching market size in an average of 25.6 months or less without your new feeding program?

b) What is the probability of a random sample of 52 market-size cod weighing an average of 3.9 kilograms or more without your new feeding program?

c) You want to examine 20 market-size cod that have achieved a weight of over 4.25 kilograms without your new feeding program. You take a random sample of 250 market-sized cod. What is the probability that this sample will contain enough cod for your purposes?