From past experience it is known that the weights of salmon grown at a commercial hatchery are normal with a mean that varies from season to season but with a standard deviation that remains fixed at 0.3 pounds.

(a) if we want to be 95 percent certain that our estimate of the present season’s mean weight of a salmon is correct to within 0.1 pounds, how large a sample is needed?

(b) for a sample of n = 35 observation, the average weight is 2.1 pounds. find a confidence interval for the true weight at level 98%.