1. Robin shoots 8 arrows at a target each day for 100 days.

The number of times he hits the target each day is summarised in the table below. Misha believes that these data can be modelled by a binomial distribution.

1. State, in context, two assumptions that are implied by the use of this model.
2. Find an estimate for the proportion of arrows Robin shoots that hit the target. Misha calculates expected frequencies, to 2 decimal places, as follows.

   Number of hits	0	1	2	3	4	5	6	7	8
   Expected frequency	2.81	12.67	\(r\)	28.05	19.73	\(s\)	2.50	0.40	0.03

3. Find the value of \(r\) and the value of \(s\) Misha correctly used a suitable test to assess her belief.
4. 1. Explain why she used a test with 3 degrees of freedom.
   2. Complete the test using a \(5 \%\) level of significance. You should clearly state your hypotheses, test statistic, critical value and conclusion.