How to find z-scores?

Question

How can I find the z-scores of 0.7491, 0.0931, and 0.3452?

Answer 1

The total area under the standardized normal distribution curve is 1.  If you have a textbook handy, there should be "Z-tables" in it that list areas under the curve to the LEFT of the Z-value. 

For Z=0, the area to the left of the curve is 0.5000, since the curve is symmetric around Z=0, the mean of the standard normal distribution.  

Let's look at the first one: 0.7491.  In the table I am looking at (yours may vary slightly), I don't have an exact match for 0.7491.  Here's what I do have:

Z = 0.67, area = 0.7486

Z = 0.68, area = 0.7517

Since the closest match to 0.7491 is 0.7486, the correct answer is Z = 0.67.  While you *could* get cute and try to interpolate between the two values, it is best to simply find the nearest value from your table.

I'll leave the other two for you to figure out; if you want to post your answers I'll be happy to look at them.

I wish I could include graphs for you-it would make things easier to understand.