6 The Body Mass Index (BMI) of each of a random sample of 100 army recruits from a large intake in 2008 was measured. The results are summarised by $$\Sigma x = 2605.0 , \quad \Sigma x ^ { 2 } = 68636.41 .$$ It may be assumed that BMI has a normal distribution.

1. Find a 98\% confidence interval for the mean BMI of all recruits in 2008.
2. Estimate the percentage of the intake with a BMI greater than 30.0.
3. The BMIs of two randomly chosen recruits are denoted by \(\boldsymbol { B } _ { 1 }\) and \(\boldsymbol { B } _ { 2 }\). Estimate \(\mathrm { P } \left( \boldsymbol { B } _ { 1 } - \boldsymbol { B } _ { 2 } < 5 \right)\).
4. State, giving a reason, for which of the above calculations the normality assumption is unnecessary.