8. A physicist believes that the number of particles emitted by a radioactive source with a long half-life can be modelled by a Poisson distribution. She records the number of particles emitted in 80 successive 5-minute periods and her results are shown in the table below.
| No. of Particles | 0 | 1 | 2 | 3 | 4 | 5 or more |
| No. of Intervals | 23 | 32 | 14 | 8 | 3 | 0 |
- Comment on the suitability of a Poisson distribution for this situation.
- Show that an unbiased estimate of the mean number of particles emitted in a 5 -minute period is 1.2 and find an unbiased estimate of the variance.
- Explain how your answers to part (b) support the fitting of a Poisson distribution.
- Stating your hypotheses clearly and using a \(5 \%\) level of significance, test whether or not these data can be modelled by a Poisson distribution.
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