A study conducted found the length of Atlantic cod to have a mean of 49.9 cm and a standard deviation of 3.74 cm. Assume the length of fish is normally distributed.

a.) State the random variable.

b.) Find the probability that an Atlantic cod has a length less than 52 cm.

c.) Find the probability that an Atlantic cod has a length of more than 74 cm.

d.) Find the probability that an Atlantic cod has a length between 40.5 and 57.5 cm.

e.) If you found an Atlantic cod to have a length of more than 74 cm, what could you conclude?

f.) What length are 15% of all Atlantic cod longer than?