CAIE S2 2022 June — Question 1

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2022
SessionJune
TopicHypothesis test of a normal distribution

1 The diameters, \(x\) millimetres, of a random sample of 200 discs made by a certain machine were recorded. The results are summarised below. $$n = 200 \quad \Sigma x = 2520 \quad \Sigma x ^ { 2 } = 31852$$
  1. Calculate a 95\% confidence interval for the population mean diameter.
  2. Jean chose 40 random samples and used each sample to calculate a 95\% confidence interval for the population mean diameter. How many of these 40 confidence intervals would be expected to include the true value of the population mean diameter?