Question 1200442
p = .39
q = 1 - .39 = .61
sample size is 203.
standard error = sqrt(.39 * .61 / 203) = .0342333344.
95% confidence interval is equal to plus or minus z = 1.959963986.
z-score formula is z = (x - m) / s
z is the z-score
x is the sample mean proportion.
m is the population mean proportion.
s is the standard error.
solve for x to get x = z * s + m which becomes:
x = -1.959963986 * .0342333344 + .39 = .3229038975 at the lower limit.
solve for x = 1.959963986 * .0342333344 + .39 = .4570961025 at the upper limit.
round to 3 decial places to get:
(.323,.457) as  your answer.
here's what it looks like, using the calculator at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>
<img src = "http://theo.x10hosting.com/2023/022003.jpg">