Question

A company that produces white bread is concerned about the distribution of the amount of sodium in its bread. How large of a sample size should the company take if they want to create a 99% confidence interval within 5 milligrams of sodium from the true mean amount of sodium in its bread. Note that the population standard deviation for the bread is assumed to be 10 milligrams.

Answer 1

Let denotes the population standard deviation for the bread. Let n be the required sample size for confidence interval to be of length 5 milligrams. Here we assume the population distribution as normal.

Since the length of (1- ) % level of confidence interval of population mean is given by

So as here = 0.01. and len = 5 millligrams, = 10 millligrams, so

So n should be 107.