CAIE S1 2010 June — Question 4

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2010
SessionJune
TopicNormal Distribution
TypeLinear relationship μ = kσ

4 The random variable \(X\) is normally distributed with mean \(\mu\) and standard deviation \(\sigma\).
  1. Given that \(5 \sigma = 3 \mu\), find \(\mathrm { P } ( X < 2 \mu )\).
  2. With a different relationship between \(\mu\) and \(\sigma\), it is given that \(\mathrm { P } \left( X < \frac { 1 } { 3 } \mu \right) = 0.8524\). Express \(\mu\) in terms of \(\sigma\).