5 The times taken by new recruits to complete an assault course may be modelled by a normal distribution with a standard deviation of 8 minutes. A group of 30 new recruits takes a total time of 1620 minutes to complete the course.

1. Calculate the mean time taken by these 30 new recruits.
2. Assuming that the 30 recruits may be considered to be a random sample, construct a \(98 \%\) confidence interval for the mean time taken by new recruits to complete the course.
3. Construct an interval within which approximately \(98 \%\) of the times taken by individual new recruits to complete the course will lie.
4. State where, if at all, in this question you made use of the Central Limit Theorem.