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# Hello all,I'm a bit stuck on how to calculate Question F) I'm just

wondering if it's a binomial or poisson approximation, or if it's something even simpler than that?

For example using the Binomial Approximation -

n = 100, p = 0.70, q = 0.30

np = 70 std dev = SQRT (100 * 0.70 * 0.30) = 4.5826

P( X equal to or greater than 0.70) = 0.80 - 0.75 / 4.5826

Z score = 0.01

= 0.50399 50.40%

Not sure if this is the right approach before proceeding onto the 0.84, 0.88 and 0.92 Mean SGR Values.

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
Chances of making a profit. A profit cannot be made under Option 1 since the process is stopped before the
salmon mature. Under Option 2, for a batch of 100 salmon to return a profit, at least seventy percent of the
salmon must have SGR levels above the minimum acceptable value of 0.75.
f) For batches of 100 salmon, compute the probabilities that the number of salmon is at least equal to 70 and
use these values to complete the table below.
Probabilities of making a profit under option 2 based on mean SGR for ten abalone for different mean levels of SGR for the tank
Mean SGR for tank
0.80
0.84
0.88
0.92
70 or more
acceptable
g) Assuming that the mean SGR is 0.84 what is the overall probability of making a profit?
h) Do you think that the decision rule used by the company is reasonable?

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