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

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 a z-score for a standard normal distribution using StatCrunch.  Here's our problem statement: Find the indicated z-score.  The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

OK, here we have a graphical depiction of a standard normal distribution curve.  Notice the indicated z-score lies to the left of 0.  That means the z-score we're looking for is negative.  We're also given the area underneath the curve that's bounded by that z-score that we're looking for.  So the simplest way to do this in StatCrunch is to go to Stat –> Calculators –> Normal.  This pulls up the Normal calculator.  Notice that the default settings for mean and standard deviation are the ones for the standard normal distribution.  These are the ones that we were instructed to use in the problem statement.

Solution

This makes solving this problem extremely easy.  All I need to do now is put this area into this field in StatCrunch.  We want the area to the left, so I need to make sure that this inequality sign drop down field is set appropriately.  This is what we want — less than or equal to — because this is like an arrow pointing in the direction that we want, and that's the direction that we want, the area to the left.  So we leave that alone.

You press Compute!, and out comes our z-score.  We are asked to round to two decimal places, so that gives me -0.62.  Well done!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below and 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 care to help you learn stats, go to aspiremountainacademy.com, where you can find out 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.