4 The masses, \(m\) kilograms, of flour in a random sample of 90 sacks of flour are summarised as follows.
$$n = 90 \quad \Sigma m = 4509 \quad \Sigma m ^ { 2 } = 225950$$
- Find unbiased estimates of the population mean and variance.
- Calculate a \(98 \%\) confidence interval for the population mean.
- Explain why it was necessary to use the Central Limit theorem in answering part (b).
- Find the probability that the confidence interval found in part (b) is wholly above the true value of the population mean.