5 The weight of fat in a digestive biscuit is known to be normally distributed.
Pat conducted an experiment in which she measured the weight of fat, \(x\) grams, in each of a random sample of 10 digestive biscuits, with the following results: $$\sum x = 31.9 \quad \text { and } \quad \sum ( x - \bar { x } ) ^ { 2 } = 1.849$$

1. 1. Construct a \(99 \%\) confidence interval for the mean weight of fat in digestive biscuits.
   2. Comment on a claim that the mean weight of fat in digestive biscuits is 3.5 grams.
2. If 200 such \(99 \%\) confidence intervals were constructed, how many would you expect not to contain the population mean?