I'm a bit confused where to start with this question of calculating the probability of 'Mean SGR for tank' and the probabilities of option 1 or option 2 being selected.

I'm guessing it's a normal approximation but I get a bit lost on the greater and lesser than thing and also if it's binomial or poisson probability.

Question 3 (18 marks)

The growth rate of salmon can be monitored using a statistic known as the specific growth rate (SGR). If the growth rate for salmon in a tank is too low, it is not economic to spend money and use resources to continue to grow the salmon. In the early stages, a sample of salmon is monitored to provide the information on which a decision will be based. There are two options:

Option 1. discard this batch and start the process again with a new batch of salmon because the growth rate is too low;

Option 2. allow the present stock to continue growing.

Decision making rule. To make a decision, a sample of fiften salmon is tagged, the mean SGR is determined for the tagged fish, and a decision is made based on the following rule:

Choose Option 1: if the mean SGR is less than 0.74.

Choose Option 2 :if the mean SGR is over 0.74.

Probabilities of choosing different options. From past observation, it is known that the pattern of SGR among individual salmon is well approximated by a Normal distribution with standard deviation 0.21

a) For the indicated mean values for SGR in the table below, complete the table to establish the probabilities that the decision rule stated above will lead to the selection of Option 1 or Option 2.

Probabilities of selecting different options based on mean SGR for fifteen salmon for different mean levels of SGR for the tank

Mean SGR for tank:

0.80 Probability = Option 1& Option 2

0.84 Probability = Option 1& Option 2

0.88 Probability = Option 1& Option 2

0.92 Probability = Option 1& Option 2