AQA Paper 3 2021 June — Question 17

Exam BoardAQA
ModulePaper 3 (Paper 3)
Year2021
SessionJune
TopicBinomial Distribution
TypeVerify conditions in context

17 James is playing a mathematical game on his computer.
The probability that he wins is 0.6
As part of an online tournament, James plays the game 10 times.
Let \(Y\) be the number of games that James wins.
17
  1. State two assumptions, in context, for \(Y\) to be modelled as \(B ( 10,0.6 )\)
    17
  2. \(\quad\) Find \(\mathrm { P } ( Y = 4 )\)
    17
  3. \(\quad\) Find \(\mathrm { P } ( Y \geq 4 )\)
    17
  4. After practising the game, James claims that he has increased his probability of winning the game. In a random sample of 15 subsequent games, he wins 12 of them.
    Test a \(5 \%\) significance level whether James's claim is correct.
    \begin{center} \begin{tabular}{|l|l|l|l|} \hline \multicolumn{4}{|c|}{\begin{tabular}{l}