A researcher wants to estimate the proportion of adult males

A researcher wants to estimate the proportion of adult males who are under 5 ft. 5 in. tall. She wants to be 99% confident that her estimate is within 2% of the true proportion. How large of a sample should be taken if in a previous study 30 of 300 males were under 5 ft. 5 in.?? PLEASE SHOW ALL CALCULATIONS AND FORMULAS PLEASE I need to know exactly how this can be done

Solution

Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.01 is = 2.576
Samle Proportion = 30/300 = 0.1
ME = 0.02
n = ( 2.576 / 0.02 )^2 * 0.1*0.9
= 1493.05 ~ 1494