AQA S1 2005 January — Question 2

Exam BoardAQA
ModuleS1 (Statistics 1)
Year2005
SessionJanuary
TopicNormal Distribution
TypeSingle tail probability P(X < a) or P(X > a)

2 The volume, in millilitres, of lemonade in mini-cans may be assumed to be normally distributed with a standard deviation of 3.5. The volumes, in millilitres, of lemonade in a random sample of 12 mini-cans were as follows.
155148156149147156
157156150154148154
  1. Construct a \(98 \%\) confidence interval for the mean volume of lemonade in a mini-can, giving the limits to one decimal place.
  2. On each mini-can is printed " 150 ml ". Comment on this, using the given sample and your confidence interval in part (a).
  3. State why, in part (a), use of the Central Limit Theorem was not necessary.