- Jim farms oysters in a particular lake. He knows from past experience that \(5 \%\) of young oysters do not survive to be harvested.
In a random sample of 30 young oysters, the random variable \(X\) represents the number that do not survive to be harvested.
- Write down a suitable model for the distribution of \(X\).
- State an assumption that has been made for the model in part (a).
- Find the probability that
- exactly 24 young oysters do survive to be harvested,
- at least 3 young oysters do not survive to be harvested.
A second random sample, of 200 young oysters, is taken. The probability that at least \(n\) of these young oysters do not survive to be harvested is more than 0.8
- Using a suitable approximation, find the maximum value of \(n\).
Jim believes that the level of salt in the lake water has changed and it has altered the survival rate of his oysters. He takes a random sample of 25 young oysters and places them in the lake.
When Jim harvests the oysters, he finds that 21 do survive to be harvested. - Use a suitable test, at the \(5 \%\) level of significance, to assess whether or not there is evidence that the proportion of oysters not surviving to be harvested is more than \(5 \%\). State your hypotheses clearly.