6. The continuous random variable \(Y\) is uniformly distributed over the interval
$$[ a - 3 , a + 6 ]$$
where \(a\) is a constant.
A random sample of 60 observations of \(Y\) is taken.
Given that \(\bar { Y } = \frac { \sum _ { i = 1 } ^ { 60 } Y _ { i } } { 60 }\)
- use the Central Limit Theorem to find an approximate distribution for \(\bar { Y }\)
Given that the 60 observations of \(Y\) have a sample mean of 13.4
- find a \(98 \%\) confidence interval for the maximum value that \(Y\) can take.