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 germinate | 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 \(\mathrm { B } ( 5 , p )\).
- Use Rosie's results to show that \(p = 0.42\).
- 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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\includegraphics[max width=\textwidth, alt={}, center]{b9cbf607-4f40-41bb-8374-6b2c39f945ac-07_2726_35_97_20}