(1) First, the confidence level is 95%, alpha= 1-0.95=0.05, and the corresponding quantile Za/2= 1.96.

BecauSE ME= 1.96*SE, in order to make ME (error amplitude) less than 0.05, let se (standard deviation)

Because SE=(p( 1-p)/n is the root number and the maximum value of p( 1-p) is 0.25 (when p = 0.5), the only unknown n in inequality should be greater than 384. 16, and the integer is 385.

(2) It is the same as the above steps, but it is known that P is (0. 1, 0.2), so the maximum value of p( 1-p) is 0.16 (when P = 0.2).

Bring 0. 16 back to the formula SE=(p( 1-p)/n) root number < 0.0255, the only unknown number n should be greater than 246.06, and the integer is 247.