CAIE S1 2011 November — Question 1

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2011
SessionNovember
TopicNormal Distribution
TypeLinear relationship μ = kσ

1 The random variable \(X\) is normally distributed and is such that the mean \(\mu\) is three times the standard deviation \(\sigma\). It is given that \(\mathrm { P } ( X < 25 ) = 0.648\).
  1. Find the values of \(\mu\) and \(\sigma\).
  2. Find the probability that, from 6 random values of \(X\), exactly 4 are greater than 25 .