AQA S2 2010 June — Question 6

Exam BoardAQA
ModuleS2 (Statistics 2)
Year2010
SessionJune
TopicDiscrete Probability Distributions
TypeCalculate E(X) from given distribution
6
  1. The number of strokes, \(R\), taken by the members of Duffers Golf Club to complete the first hole may be modelled by the following discrete probability distribution.
    \(\boldsymbol { r }\)\(\leqslant 2\)345678\(\geqslant 9\)
    \(\mathbf { P } ( \boldsymbol { R } = \boldsymbol { r } )\)00.10.20.30.250.10.050
    1. Determine the probability that a member, selected at random, takes at least 5 strokes to complete the first hole.
    2. Calculate \(\mathrm { E } ( R )\).
    3. Show that \(\operatorname { Var } ( R ) = 1.66\).
  2. The number of strokes, \(S\), taken by the members of Duffers Golf Club to complete the second hole may be modelled by the following discrete probability distribution.
    \(\boldsymbol { s }\)\(\leqslant 2\)345678\(\geqslant 9\)
    \(\mathbf { P } ( \boldsymbol { S } = \boldsymbol { s } )\)00.150.40.30.10.030.020
    Assuming that \(R\) and \(S\) are independent:
    1. show that \(\mathrm { P } ( R + S \leqslant 8 ) = 0.24\);
    2. calculate the probability that, when 5 members are selected at random, at least 4 of them complete the first two holes in fewer than 9 strokes;
    3. calculate \(\mathrm { P } ( R = 4 \mid R + S \leqslant 8 )\).
      \includegraphics[max width=\textwidth, alt={}]{c31c5c67-834e-42ce-b4af-555890c393d5-15_2484_1709_223_153}
      \includegraphics[max width=\textwidth, alt={}]{c31c5c67-834e-42ce-b4af-555890c393d5-16_2484_1712_223_153}
      \includegraphics[max width=\textwidth, alt={}]{c31c5c67-834e-42ce-b4af-555890c393d5-17_2484_1709_223_153}
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