CAIE S1 2011 June — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2011
SessionJune
TopicNormal Distribution
TypeQuadratic relationship μ = kσ²

5
  1. The random variable \(X\) is normally distributed with mean \(\mu\) and standard deviation \(\sigma\). It is given that \(3 \mu = 7 \sigma ^ { 2 }\) and that \(\mathrm { P } ( X > 2 \mu ) = 0.1016\). Find \(\mu\) and \(\sigma\).
  2. It is given that \(Y \sim \mathrm {~N} ( 33,21 )\). Find the value of \(a\) given that \(\mathrm { P } ( 33 - a < Y < 33 + a ) = 0.5\).