How do you find the 95% confidence interval?

The confidence interval is given by the formula:

#barx +-z(sigma/sqrtn)#

Or you can write it as:

#(barx -z(sigma/sqrtn),barx +z(sigma/sqrtn))#

Where #barx# is the sample mean, #z# is the standardized value for the normal distribution, in relation to the percentage (don't really know how to explain this one that well), #sigma# is the standard deviation, and #n# is the sample size.

We know all the values except for #z#. To find the #z# value, we can imagine a normal distribution graph with 95% of it shaded, where the middle of this is the mean.

As you can see from this picture the #z# value is 1.96. This can be found by using a normal distribution percentage points look up table.
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:

#(20.3 -1.96(10.2/sqrt39),20.3 +1.96(10.2/sqrt39))#

Enter this into your calculator and you get:

#(17.1, 23.5)#

Hope this helps!