5 The masses, \(m\) grams, of a random sample of 80 strawberries of a certain type were measured and summarised as follows.
$$n = 80 \quad \Sigma m = 4200 \quad \Sigma m ^ { 2 } = 229000$$
- Find unbiased estimates of the population mean and variance.
- Calculate a 98\% confidence interval for the population mean.
50 random samples of size 80 were taken and a \(98 \%\) confidence interval for the population mean, \(\mu\), was found from each sample.
- Find the number of these 50 confidence intervals that would be expected to include the true value of \(\mu\).