AQA Further Paper 3 Statistics 2019 June — Question 3

Exam BoardAQA
ModuleFurther Paper 3 Statistics (Further Paper 3 Statistics)
Year2019
SessionJune
TopicNormal Distribution
TypeSingle tail probability P(X < a) or P(X > a)

3 Alan's journey time to work can be modelled by a normal distribution with standard deviation 6 minutes. Alan measures the journey time to work for a random sample of 5 journeys. The mean of the 5 journey times is 36 minutes. 3
  1. Construct a 95\% confidence interval for Alan's mean journey time to work, giving your values to one decimal place.
    3
  2. Alan claims that his mean journey time to work is 30 minutes.
    State, with a reason, whether or not the confidence interval found in part (a) supports Alan's claim.
    3
  3. Suppose that the standard deviation is not known but a sample standard deviation is found from Alan's sample and calculated to be 6 Explain how the working in part (a) would change.