It is claimed that 22% of people in the UK have brown eyes. A sample of 50 people finds that 15 have brown eyes. (a) Based on the sample, find a 95% confidence interval for the percentage of people with brown eyes in the UK. (6 marks) (b) State with a reason whether or not your interval supports the claim. (1 marks) (c) Assume that the true percentage is 27%, how large a sample is needed in order to estimate the percentage of people with brown eyes in the UK to within +1% points with 95% confidence