OCR S2 Specimen — Question 4

Exam BoardOCR
ModuleS2 (Statistics 2)
SessionSpecimen
TopicNormal Distribution
TypeFind standard deviation from probability

4 The random variable \(G\) has mean 20.0 and standard deviation \(\sigma\). It is given that \(\mathrm { P } ( G > 15.0 ) = 0.6\). Assume that \(G\) is normally distributed.
  1. (a) Find the value of \(\sigma\).
    (b) Given that \(\mathrm { P } ( G > g ) = 0.4\), find the value of \(\mathrm { P } ( G > 2 g )\).
  2. It is known that no values of \(G\) are ever negative. State with a reason what this tells you about the assumption that \(G\) is normally distributed.