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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.
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