The 95% confidence interval based on a sample with s = 15 extends from 31.4 to 37.4. what is the size of the sample? urgent :

ould use the margin of error formula so that we can solve for the sample size yielding necessary results for an accurate specified confidence and margin of error.

The formula for margin of error is:

E = Za/2 * standard deviation / sqrt n

So we are going to change this into

n = [Za/2 * standard dev / Margin of error] ^2

so for a 95% confidence interval we have an alpha equivalent to = 0.05

so a/2 = 0.025. the critical value for this is 1.960

let our margin of error be 1 and the standard deviation be 1

so plugging in our data:

n = [1.96 * 15 / 1] ^2

= 864.36 or 864

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls