ASRJC Sampling Tutorial Q5

A random sample of \(100\) packets of a breakfast cereal was examined and the mass, \(m\) grams, of the contents recorded. The results revealed that \(\sum{m=3010}\) and \(\sum{{{m}^{2}}=91\,280}\). Obtain an unbiased estimate of the population variance.[2]

By taking the unbiased estimate obtained above to be the population variance, find the size of the random sample required so that there is a probability of at least \(0.98\) that the sample mean will be within \(0.5\)g of the true mean.[5]