2 The weights in grams of oranges grown in a certain area are normally distributed with mean \(\mu\) and standard deviation \(\sigma\). A random sample of 50 of these oranges was taken, and a \(97 \%\) confidence interval for \(\mu\) based on this sample was (222.1, 232.1).

1. Calculate unbiased estimates of \(\mu\) and \(\sigma ^ { 2 }\).
2. Estimate the sample size that would be required in order for a \(97 \%\) confidence interval for \(\mu\) to have width 8 .