5 The volumes, \(v\) millilitres, of juice in a random sample of 50 bottles of Cooljoos are measured and summarised as follows.
$$n = 50 \quad \Sigma v = 14800 \quad \Sigma v ^ { 2 } = 4390000$$
- Find unbiased estimates of the population mean and variance.
- An \(\alpha \%\) confidence interval for the population mean, based on this sample, is found to have a width of 5.45 millilitres. Find \(\alpha\).
Four random samples of size 10 are taken and a \(96 \%\) confidence interval for the population mean is found from each sample.
- Find the probability that these 4 confidence intervals all include the true value of the population mean.