# Thread: 85% Confidence Intervals... Z-value?

1. ## 85% Confidence Intervals... Z-value?

I'm looking over corrections for one of my midterms and ran into a few problems giving me weird Z-values from confidence intervals that don't exactly correspond to my Cumulative T Distribution Table.

Question
A sample of 19 eggs of the Atlantic Fairy Tern are each measured. The mean diameter is 3.34 cm. The actual population standard deviation of the diameter is 0.2 cm, what is the lower limit of an 85% confidence interval on the mean?
How do I calculate the Z value required? The answer it gives me is Za/2=1.44 but I have no clue why and can't find "Za/2" anywhere in my notes to determine how all of this works.

Thanks!

2. You Z-value looks fine, which you can use as the population standard deviation is known.

You are after the lower bound so

$\displaystyle \displaystyle \bar{x}-Z_{\frac{\alpha}{2}}\times \frac{\sigma}{\sqrt{n}} = 3.34-Z_{\frac{0.15}{2}}\times \frac{0.2}{\sqrt{19}} = 3.34-1.4395\times \frac{0.2}{\sqrt{19}} =\dots$

Remember $\displaystyle t\to z$ as $\displaystyle n$ gets large

3. Thanks, but I know it's right... I just don't know why.

Where did the 1.44 (or 1.4395) come from? How would I find Z0.15/2 on a standard normal table? Or would I?

4. Originally Posted by QNev
Where did the 1.44 (or 1.4395) come from? How would I find Z0.15/2 on a standard normal table? Or would I?
Thanks how I found it!

This is a good one

Z table - Normal Distribution

Find area under the curve to be 0.85 and "between" this should illustrate why.

5. Thanks for the link but that's no good on a final haha. I have tables with values for a tail with areas of .10, .05, .1, .05, .005, etc. but not some weird in-between values like .075 and .02 and stuff like that. I would love to find out a formula for these but I can't find it anywhere.

6. Originally Posted by QNev
Thanks for the link but that's no good on a final haha. I have tables with values for a tail with areas of .10, .05, .1, .05, .005, etc. but not some weird in-between values like .075 and .02 and stuff like that. I would love to find out a formula for these but I can't find it anywhere.
Most tables won't have these stange values, you can approximate between known values.

Are you allowed to use a graphing calculator?

7. Originally Posted by QNev
Thanks for the link but that's no good on a final haha. I have tables with values for a tail with areas of .10, .05, .1, .05, .005, etc. but not some weird in-between values like .075 and .02 and stuff like that. I would love to find out a formula for these but I can't find it anywhere.
You interpolate in the table you are given, if your table is for the cumulative standard normal you will want to look up the z-score for a tail probability of 0.075, which you get by interpolation between the values for tail probability 0.1 and 0.05.

CB

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# confidence interval of 85%

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