CAIE Further Paper 4 2024 November — Question 3

Exam BoardCAIE
ModuleFurther Paper 4 (Further Paper 4)
Year2024
SessionNovember
TopicChi-squared distribution

3 Rosie sows 5 seeds in each of 150 plant pots. The number of seeds that germinate is recorded for each pot. The results are summarised in the following table.
Number of seeds that germinate012345
Number of pots12404335164
Rosie suggests that the number of seeds that germinate follows the binomial distribution \(\mathrm { B } ( 5 , p )\).
  1. Use Rosie's results to show that \(p = 0.42\).
  2. Carry out a goodness of fit test, at the \(10 \%\) significance level, to test whether the distribution \(\mathrm { B } ( 5,0.42 )\) is a good fit for the data.
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