# Confidence interval

#### Suzy

##### New Member
John,
Thanks for defining (interpreting) confidence intervals in language that I can understand! I am using a textbook that is really confusing to me. I have a question. If the 99% confidence interval for a population is between two numbers (such as .30 and .40), is it possible to find the value of x-bar? There's not enough information here, right? x-bar wouldn't be .35, is that correct?
Thanks.
-Suzy

#### JohnM

##### TS Contributor
If the confidence interval is for the population mean, then it's pretty safe to assume that the distribution of the sample means will be normal (or approaching normal as n increases), and so therefore the confidence interval is symmetric around x-bar.

So x-bar would be .35

#### Suzy

##### New Member
Confidence interval-Thanks!

Thanks for the quick reply. Now I'm trying to figure another problem. I read your formula to calculate confidence intervals, and I almost have this one solved. But how do I find the Z Score?
Here's the problem:
A student would like to find out the average time per week that freshman at her college spend watching TV. She collects info from a random sample of 50 freshman. The data reveals that those 50 students on an average watch 25 hours of TV per week and the standard deviation of the data was 3 hours. Find the 90% confidence interval for the mean time per week that freshman at that college spend watching TV.
This is how I've done so far:
25 +/- [Z*3/SQRT(50)]. But now I don't know how to find the value of Z. Sorry for the stupid question.
Thanks.
-S

#### JohnM

##### TS Contributor
Using the normal distribution tables, find the Z score that divides the "middle" 90% of the curve from the "outer" 10%.

It should be 1.645.

#### Suzy

##### New Member
Oh, Okay. How easy. I didn't know which table to use. Thanks, I really appreciate your help.