CAIE S2 2024 November — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2024
SessionNovember
TopicLinear combinations of normal random variables
TypeSingle normal population sample mean

4 A population is normally distributed with mean 35 and standard deviation 8.1 . A random sample of size 140 is chosen from this population and the sample mean is denoted by \(\bar { X }\).
  1. Find \(\mathrm { P } ( \bar { X } > 36 )\).
  2. It is given that \(\mathrm { P } ( \bar { X } < a ) = 0.986\). Find the value of \(a\).