4 Diameters of golf balls are known to be normally distributed with mean \(\mu \mathrm { cm }\) and standard deviation \(\sigma \mathrm { cm }\). A random sample of 130 golf balls was taken and the diameters, \(x \mathrm {~cm}\), were measured. The results are summarised by \(\Sigma x = 555.1\) and \(\Sigma x ^ { 2 } = 2371.30\).

1. Calculate unbiased estimates of \(\mu\) and \(\sigma ^ { 2 }\).
2. Calculate a \(97 \%\) confidence interval for \(\mu\).
3. 300 random samples of 130 balls are taken and a \(97 \%\) confidence interval is calculated for each sample. How many of these intervals would you expect not to contain \(\mu\) ?