1. Lecture 21 Section 6.3.1 – 6.3.2 Fri, Feb 22, 2008
Normal Percentiles
Lecture 21
Section – 6.3.2
Fri, Feb 22, 2008

2. Standard Normal Percentiles
Given a value of Z, we know how to find the area to the left of that value of Z.
Value of z  Area to the left
The problem of finding a percentile is exactly the reverse:
Given the area to the left of a value of Z, find that value of Z?
Area to the left  Value of z

3. Standard Normal Percentiles
What is the 90th percentile of Z?
That is, find the value of Z such that the area to the left is
On the TI-83, use the invNorm function.

4. Standard Normal Percentiles on the TI-83
To find a standard normal percentile on the TI-83,
Press 2nd DISTR.
Select invNorm (Item #3).
Enter the percentage as a decimal (i.e., the area).
Press ENTER.

5. Practice Use the TI-83 to find the following percentiles.
Find the 99th percentile of Z.
Find the 1st percentile of Z.
Find Q1 and Q3 of Z.
The value of Z that cuts off the top 20%.
The values of Z that determine the middle 30%.

6. Normal Percentiles
To find a percentile of a variable X that is N(, ),
Find the percentile for Z.
Use the equation X =  + Z to find X.

7. Example Assume that IQ scores are N(100, 15).
Find the 90th percentile of IQ scores.
The 90th percentile of Z is
Therefore, the 90th percentile for IQ scores is
100 + (1.282)(15) =
90% of IQ scores are below

8. TI-83 – Normal Percentiles
Use the TI-83 to find the standard normal percentile and use the equation X =  + Z.
Or, use invNorm and specify  and .
invNorm(0.90, 100, 15) =

9. Practice Find the 80th percentile of IQ scores.
Find the first and third quartiles of IQ scores.