# How do you find the 95% confidence interval?

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Find the 95% confidence interval for a sample of size 39 with a mean of 20.3 and a standard deviation of 10.2.

Find the 95% confidence interval for a sample of size 39 with a mean of 20.3 and a standard deviation of 10.2.

##### 1 Answer

A 95% confidence interval with the given data gives:

#### Explanation:

The confidence interval is given by the formula:

Or you can write it as:

Where

We know all the values except for

As you can see from this picture the

I hope you can see that to the left and right of the shaded area, 2.5% is taken up by the white space each side.

So therefore you do 95%+2.5% = 97.5% then you can look that value up in the tables which is in fact: 1.96.

Now you can just substitute all the numbers into the expression:

Enter this into your calculator and you get:

Hope this helps!