CAIE S1 2011 June — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2011
SessionJune
TopicNormal Distribution
TypeFind p then binomial probability

5 The random variable \(X\) is normally distributed with mean \(\mu\) and standard deviation \(\frac { 1 } { 4 } \mu\). It is given that \(\mathrm { P } ( X > 20 ) = 0.04\).
  1. Find \(\mu\).
  2. Find \(\mathrm { P } ( 10 < X < 20 )\).
  3. 250 independent observations of \(X\) are taken. Find the probability that at least 235 of them are less than 20.