6. The continuous random variable \(X\) is uniformly distributed over the interval
$$[ a - 1 , a + 5 ]$$
where \(a\) is a constant.
Fifty observations of \(X\) are taken, giving a sample mean of 17.2
- Use the Central Limit Theorem to find an approximate distribution for \(\bar { X }\).
- Hence find a 95\% confidence interval for \(a\).