Finding a z-score for a standard normal distribution using a table

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find the z-score for a standard normal distribution using a table.  Here's our problem statement: Find the indicated z-score.  The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

Solution

OK. We're looking for a z-score, and notice the z-value or z-score that we're looking at over here is on the right side of the distribution.  That means the z-score is going to have a positive value.  If the z-score were directly in the middle, the z-value or z-score would be zero.  If it were to the left, on the left side of the distribution, then it would be negative.  But here we find it on the right side, so therefore it's going to be positive.

That means we want the second page of our table, because the first page of the table lists the negative z-score values.  We want a positive z-score because it's here on the right.  So here's my table.  Notice it's the areas that are listed under here in the table, which are also the same as the this which correlate with the z-scores.  So that area is to the left of the z-score.

That's exactly what we have here in our problem statement.  This area under the curve, which is 0.9817, is to the left of the z-score we're looking for.  So here we're going to look in the table for this value (0.9817) and then get the corresponding z-score.  So 0.9817 --- if I look here in my table, you gotta scroll down --- 0.98 ... 0.9817.  OK, so here's the 0.9817.

So remember the z-scores are listed in two parts.  The first part is over here on the left.  So I go over here to the left.  Here's the first part: 2.0.  And then the last part is going to be up here at the label for the column, 0.09.  So we add those two together, and we get 2.09.  So there's the first part ... 2.09.  That's my z-score.  So I put that here in my answer field.  Good job!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below.  Let us know how good a job we did or how we can improve.  And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see.  Thanks for watching!  We'll see you in the next video.