9231 P42 - Nov 2024 - Q3 - 10 marks
6847
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.
| 0 | 1 | 2 | 3 | 4 | 5 | ||
|---|---|---|---|---|---|---|---|---|
Number of pots | 12 | 40 | 43 | 35 | 16 | 4 | ||
Rosie suggests that the number of seeds that germinate follows the binomial distribution \(\mathrm{B}(5, p)\).
(a) Use Rosie's results to show that \(p=0.42\).
(b) 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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