# The size of fish is very impor

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. Assume the length of fish is normally distributed. A sample of 17 fish was taken.

d) Find the mean of the sampling distribution of the sample mean.

Put the numeric value in the first box and the correct units in the second box.

e) Find the standard deviation of the sampling distribution of the sample mean.

Put the numeric value rounded to two decimal places in the first box and the correct units in the second box.

g) Find the probability that the sample mean length of the 17 randomly selected Atlantic cod is less than 51.5 cm.

Round final answer to 4 decimal places.

DO NOT use the rounded standard deviation from part e in this computation.

Use the EXACT value of the standard deviation with the square root.

h) Find the probability that the sample mean length of the 17 randomly selected Atlantic cod is more than52.33 cm.

Round final answer to 4 decimal places.

DO NOT use the rounded standard deviation from part e in this computation.

Use the EXACT value of the standard deviation with the square root.

# The size of fish is very impor

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. A sample of 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 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?

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