Please provide detailed explanation for these questions. I don't understand how to find out the equation for solving n.

(b) Suppose that the binomial distribution parameter 7 is to be estimated by P = X, where X is the number of successes in n independent trials, i.e. P is the sample proportion of successes. i. Write down the endpoints of an approximate 100(1 - a)% confidence interval for 7, stating any necessary conditions which should be satisfied for such an approximate confidence interval to be used. You should also state the approximate sampling distribution of P = X. (5 marks) ii. Suppose we are willing to assume that 00. ii. Take 12. to be the smallest integer such that: > (20.005)27r(1 7T) _ (2.576)2 X 0.40 X 0.60 = 637.03 \" (0.05)2 (0.05)2 hence it = 638