The size of fish is very important to commercial fishing. A study conducted in

2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean

of 49.9 cm and a standard deviation of 3.74 cm (Ovegard, Berndt & Lunneryd,

2012). The length of fish is normally distributed. Asampleof 15 fish is taken.

a.) State the random variable.

b.) Find the mean of the sample mean.

c.) Find the standard deviation of the sample mean

d.) What is the shape of the distribution of the sample mean? Why?

e.) Find the probability that the sample mean length of the Atlantic cod is less

than 52 cm.

f.) Find the probability that the sample mean length of the Atlantic cod is more

than 74 cm.

g.) If you found sample mean length for Atlantic cod to be more than 74 cm, what

could you conclude?