Question 1187550
p = 177 / 300 = .59
q = 1 - p = .41


mean proportion = p = .59


standard error = sqrt(p * (1-p / 300) = sqrt(.59 * .41 / 300) = .028396.


critical z-score at 90% confidence level is plus or minus 1.645.


use the z-score formula to find the critical raw score.


for the low side, z = (x - m) / s becomes:


-1.645 = (x - .59) / .028396.

solve for x to get:


x = -1.645 * .0283960091 + .59 = .54329.


for the high side, z = (x - m) / s becomes:


1.645 = (x - .59) / .028396.


solve for x to get:


x = 1.645 * .028396. + .59 = .63671.


at 90% confidence level, your proportion will be between .54329 and .63671, when you have a mean of .59 and a standard error of .028396.


here's what it looks like on a z-score normal distribution calculator output.


<img src = "http://theo.x10hosting.com/2021/112506.jpg" >


the calculator i used can be found at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>