Out of a random sample of 1000 French people interviewed during Autumn 1996, 410 supported a single European Currency.

(a) Calculate an approximate 99% confidence interval for the population proportion, p, of French people who supported a single European Currency.

(b) Estimate the size of a sample that would have provided a 99% confidence interval of width 0.04 for p.

(c) Give one reason (other than rounding) why your answer to

(b) is only an estimate. (C)