OCR S2 2014 June — Question 3 7 marks

Exam BoardOCR
ModuleS2 (Statistics 2)
Year2014
SessionJune
Marks7
TopicNormal Distribution
TypeEstimate from percentile/frequency data

3 The random variable \(G\) has the distribution \(\mathbf { N } \left( \mu , \boldsymbol { \sigma } ^ { 2 } \right)\). One hundred observations of \(G\) are taken. The results are summarised in the following table.
Interval\(G < 40.0\)\(40.0 \leqslant G < 60.0\)\(G \geqslant 60.0\)
Frequency175825
  1. By considering \(\mathrm { P } ( G < 40.0 )\), write down an equation involving \(\mu\) and \(\sigma\). [2]
  2. Find a second equation involving \(\mu\) and \(\sigma\). Hence calculate values for \(\mu\) and \(\sigma\). [4]
    [0pt]
  3. Explain why your answers are only estimates. [1]