Edexcel S3 2024 June — Question 7

Exam BoardEdexcel
ModuleS3 (Statistics 3)
Year2024
SessionJune
TopicCentral limit theorem
TypeDistribution of sample mean

  1. 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.
  1. 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,
  2. find the value of \(n\) Show your working clearly.