3. A large number of chicks were fed a special diet for 10 days. A random sample of 9 of these chicks is taken and the weight gained, \(x\) grams, by each chick is recorded. The results are summarised below. $$\sum x = 181 \quad \sum x ^ { 2 } = 3913$$ You may assume that the weights gained by the chicks are normally distributed.
Calculate a 95\% confidence interval for

1. 1. the mean of the weights gained by the chicks,
   2. the variance of the weights gained by the chicks. A chick which gains less than \(16 g\) has to be given extra feed.
2. Using appropriate confidence limits from part (a), find the lowest estimate of the proportion of chicks that need extra feed.