normal distribution using excel

B Heard

Bonus Lecture for ProblemsDealing with the Normal

Distribution

Statistics For Decision Making

Not to be used, posted, etc. without my expressed permission. B Heard

No Audio with this presentation, but this should be very helpful – trust me

In looking at the normal distribution, we are going to learn to use a template based on the normal distribution

We will work on a problem related to the height of 12 year-old boys

Normal Distribution Bonus Lecture




Before we get started go to:http://

highered.mcgraw-hill.com/sites/0070620164/student_view0/excel_templates.html

and download (Save) the “Normal Distribution” Excel File

http://highered.mcgraw-hill.com/sites/0070620164/student_view0/excel_templates.html





Now on your computer open the file you saved

The first thing you need to do is go to the Review Tab and click “Unprotect Sheet”



Now your template should look like this



Let’s say that we have data to prove that 12 year-old boys heights are normally distributed with:

Mean = 64 inchesStandard Deviation = 5 inches

Let’s enter those values in the template and clear the old data left in the original template example. Your template should now look like the one that follows on the next slide.



Using the template we are going to answer the following questions:

1) What is the probability that a 12 year-old boy is shorter than 58 inches?

2) What is the probability that a 12 year-old boy is taller than 67 inches?

3) What is the probability that a 12 year-old boy is between 60 and 66 inches tall?

4) What height marks the top 10% of 12 year-old boys?

5) 50% of all 12 year-old boys are between what two heights (equally distributed from the mean)?



1) What is the probability that a 12 year-old boy is shorter than 58 inches?

Notice we use the top left option because from the cartoon you can see this gives the probability that it is below the value you put in the green box. Entering 58 gives us the probability 0.1151 that he is shorter than 58 inches.



2) What is the probability that a 12 year-old boy is taller than 67 inches?

Notice we use the top middle option because from the cartoon you can see this gives the probability that it is above the value you put in the green box. Entering 67 gives us the probability 0.2743 that he is taller than 67 inches.



3) What is the probability that a 12 year-old boy is between 60 and 66 inches tall?

Notice we use the top right option because from the cartoon you can see this gives the probability that it between the two values you put in the green boxes. Entering 60 and 66 gives us the probability 0.4436 that he is between 60 and 66 inches.



4) What height marks the top 10% of 12 year-old boys?

Notice we could use either the bottom left or bottom middle options on this one. I could have entered 0.9 in the left one or 0.1 in the middle one. Both of these give us the height we are looking for. (Where 90% of the heights are below and 10% are above) You can see the answer is 70.41 inches.



5) 50% of all 12 year-old boys are between what two heights (equally distributed from the mean)?

Notice we use the bottom right option because from the cartoon you can see this gives the values where you have a probability of 50% is distributed equally on either side of the mean. You would just put 0.5 in the green box and get your boundaries of 60.6 and 67.4 (rounded).(You probably won’t see any of these, but I wanted to tell you what it was)



• We really don’t cover Normal approximations in this class so you don’t have to worry with the second tab at the bottom



• Remember this is for the Normal Distribution only

• Always try some examples from the book and verify that you are getting correct results.

• You only enter information into the green boxes (don’t change the others)

• You can also use this template for the standard normal distribution (Z-Scores etc.) – See the following page


For the Standard Normal Distribution you would enter a Mean of 0 and Standard Deviation of 1. Working clockwise starting from the top left. This would give you the probability that is below a z-score of 1.2. Next you see the probability that is above a z-score of 1.5. Next the probability that you are between z-scores of -0.5 and 0.75. With the Inverse Calculations you get the z-score associated with the probability of 0.3258 (below) and 0.1 or 10% (above)



The best way to learn to use any of these templates successfully is to just play around with them and work problems that you have verified results through working by hand or examples in your textbook with complete solutions.

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normal distribution using excel

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