5. A research station is doing some work on the germination of a new variety of genetically modified wheat.
They planted 120 rows containing 7 seeds in each row.
The number of seeds germinating in each row was recorded. The results are as follows
| Number of seeds germinating in each row | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Observed number of rows | 2 | 6 | 11 | 19 | 25 | 32 | 16 | 9 |
- Write down two reasons why a binomial distribution may be a suitable model.
- Show that the probability of a randomly selected seed from this sample germinating is 0.6
The research station used a binomial distribution with probability 0.6 of a seed germinating. The expected frequencies were calculated to 2 decimal places. The results are as follows
| Number of seeds germinating in each row | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Expected number of rows | 0.20 | 2.06 | \(s\) | 23.22 | \(t\) | 31.35 | 15.68 | 3.36 |
- Find the value of \(s\) and the value of \(t\).
- Stating your hypotheses clearly, test, at the \(1 \%\) level of significance, whether or not the data can be modelled by a binomial distribution.