In lobster fisheries there are both minimum size limits to protect juveniles, and maximum size limits to protect breeding adults. Only lobsters between these size limits can be harvested. Regulations set the minimum and maximum size limits at 10.0 cm and 17.0 cm carapace length, respectively. Assume carapace length is normally distributed with a mean of 14.0 cm and a standard deviation of 3.8 cm.

a) What percentage of lobsters can be kept if they are caught randomly? (5 marks)

b) The mean size noted above will only be maintained if regulations are followed by the lobster fishers. To determine if this is the case, the regulatory authority routinely randomly catches, measures, and releases lobsters. In one such instance the authorities catch 20 lobsters and obtain a mean of 15.1 cm and a standard deviation of 4.3 cm. Conduct a statistical analysis. (6 marks)