- The continuous random variable \(D\) is uniformly distributed over the interval \([ x - 1 , x + 5 ]\) where \(x\) is a constant.
A random sample of \(n\) observations of \(D\) is taken, where \(n\) is large.
- Use the Central Limit Theorem to find an approximate distribution for \(\bar { D }\) Give your answer in terms of \(n\) and \(x\) where appropriate.
The \(n\) observations of \(D\) have a sample mean of 24.6
Given that the lower bound of the \(99 \%\) confidence interval for \(x\) is 22.101 to 3 decimal places, - find the value of \(n\)
Show your working clearly.