OCR H240/02 2018 June — Question 8

Exam BoardOCR
ModuleH240/02 (Pure Mathematics and Statistics)
Year2018
SessionJune
TopicNormal Distribution
TypeLinear relationship μ = kσ

8
  1. The variable \(X\) has the distribution \(\mathrm { N } ( 20,9 )\).
    (a) Find \(\mathrm { P } ( X > 25 )\).
    (b) Given that \(\mathrm { P } ( X > a ) = 0.2\), find \(a\).
    (c) Find \(b\) such that \(\mathrm { P } ( 20 - b < X < 20 + b ) = 0.5\).
  2. The variable \(Y\) has the distribution \(\mathrm { N } \left( \mu , \frac { \mu ^ { 2 } } { 9 } \right)\). Find \(\mathrm { P } ( Y > 1.5 \mu )\).