A doctor wishes to investigate the mean fat content in low-fat burgers. He takes a random sample of 15 burgers and sends them to a laboratory where the mass, in grams, of fat in each burger is determined. The results are as follows.

9,  7,  8,  9,  6,  11,  7,  9,  8,  9,  8,  10,  7,  9

Assume that the mass, in grams, of fat in low-fat burgers is normally distributed with mean $\mu $ and that the population standard deviation is 1.3.

a) Calculate a 99% confidence interval for $\mu $.

b) Explain whether it was necessary to use the Central Limit theorem in the calculation in part (a).

c) The manufacturer claims that the mean mass of fat in burgers of this type is $8{\text{ }}g$. Use your answer to part (a) to comment on this claim.