x = population proportion of an outcome, P = number of case / number ofsample, arcsin transformation of P is normal as follow:Y = arcsin(P^(1/2)) ~ N(arcsin(x^(1/2)),1/4n).

1. Formula for 90% confidence interval for w = arcsin(x^(1/2)), and use this to calculate the formula for 90% confidence interval for x?

2. Calculate 90% confidence interval for x by two ways (i. part a; ii. normal standard method ) in

a. 201 cases in sample size of 2000

b. 2 cases in sample size of 80