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## Normal Percentiles

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### Therefore, the 90th percentile for IQ scores is. 100 (1.282)(15) = 119.2. 90% of IQ scores are below 119.2. TI-83 Normal Percentiles ... – PowerPoint PPT presentation

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Title: Normal Percentiles

1
Normal Percentiles
• Lecture 21
• Section 6.3.1 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 0.9000.
• 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 1.282.
• Therefore, the 90th percentile for IQ scores is
• 100 (1.282)(15) 119.2.
• 90 of IQ scores are below 119.2.

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) 119.2.

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