Finding the area under a normal distribution curve 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 the area under a normal distribution curve using StatCrunch.  Here's our problem statement: Find the area of the shaded region.  The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

Solution

OK, to find the area for the shaded region, we could use the tables that we have links to here in the problem.  But I find it's much easier to just use StatCrunch instead of the tables for solving a problem like this.  We can use the tables, but it requires us to find the area under the curve to the left of each value and then subtract the one from the other to get the area in between.  With StatCrunch, all you do is just put the numbers in the calculator and it does all that hard heavy lifting for you.  So that's what we're going to do to solve this problem.

So I'm going to open up StatCrunch.  And I don't necessarily need anything in the data table.  I just need the functionality that StatCrunch provides so I can get into that calculator for my distribution.  It says the scores are normally distributed, so I want the normal calculator.  To get that, I go to Stat --> Calculators --> Normal.

Now here it says that the mean of the distribution is 100 and the standard deviation is 15. So I'm going to put those values in here in my calculator.  And I'm looking for the area in between two values.  So I want to come up here and select the Between option.  And then I just come down here and put those two values that I want to get the area in between.  And when I press Compute!, out comes the area in between those two values.  That is the area in between the shaded region, which is same as the probability of selecting something between those two values.  So I'm going to put my answer in my answer field.  Good job!

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