I need help with the following questions :-

Many cheeses are produced in the shape of a wheel. Because of slight variations in the consistency of a cheese, the average weight varies from wheel to wheel. The production output is supposed to have an average weight of at least 500g per wheel and samples are taken to check this. One random sample of 16 wheels of Brie cheese had a mean weight of 515.5 grams with a standard deviation of 66.5 grams. The populations of the cheeses are known to have a normal distribution of weights.

Questions :-

a) Find the point estimate of the mean weight of cheese wheel.

b) Find and interpret the 90% confidence interval for the mean weight of cheese wheel.

c) Use your answer in b) to determine if the sample shows that the production output does not have the correct average weight per wheel. d) To halve the margin of error for the sample above, what sample size would be required?