In this case, we will use our Pythagorean Theorem.
a = 84
b = 13
c = x

Thus,
x = 85.
Answer: (80% , 85%)
Step-by-step explanation:
We know that, confidence interval for population proportion is given by :-
(p-E , p+E)
, where p = sample proportion , E = Margin of error.
Given : Proportion of elementary school teachers who are female = 82%.
The article also states the maximum error of their estimate = 3%.
Then, the 90% confidence interval for the proportion of elementary school teachers who are female will be :
(82%-2% , 82%+3%)
= (80% , 85%)
Hence, the resulting 90% confidence interval for the proportion of elementary school teachers who are female = (80% , 85%)