What is the z-score associated with the 75th percentile of a normal distribution? Draw the standard normal curve using the z-scale associated with the problem.

Answer 1

There are Z tables that show the positive side, if you do a search on Z table you can find some online.

I found one that shows the following:

Z value Table entry

0.67 0.7486

0.68 0.7517

So the Z value for 0.75 is somewhere between 0.67 and 0.68.

If we interpolate we find that the z value is 0.6745

If you have a TI-84 calculator you can find the z value:

1. 2nd - VARS (this will show the DISTR menu)
2. Press 3 to select invNorm
3. Enter the area/table value (0.75)
4. Press enter and it will return the z value

Answer 2

Hello Anthony,

In order to find the answer to this question you need a z-table. Since we're looking at the top 75th percentile, but there's no 0.75 on a z-table, we are looking at the last 25% of the curve. If you look for the closest thing to 0.25 (25%÷100) on your z-table under the "beyond the tail" column, you see that the corresponding z-score is 0.67. To draw this chart, you need to shade in the area under the curve representing the 75th percentile which I can't show on here.

Thanks,

Meagan