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Normal Percentiles

Normal Percentiles. Lecture 24 Section 6.3.1 – 6.3.2 Wed, Feb 28, 2007. 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:

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Normal Percentiles

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  1. Normal Percentiles Lecture 24 Section 6.3.1 – 6.3.2 Wed, Feb 28, 2007

  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. • Table: Look up 0.9000 as an entry in the standard normal table. Read the value of Z. • 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. • 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. The Standard Normal Table • Use the normal table 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%.

  7. 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.

  8. Example • Assume that IQ scores are N(100, 15). • Find the 90th percentile of IQ scores. • The 90th percentile of Z is 1.28. • Therefore, the 90th percentile for IQ scores is 100 + (1.28)(15) = 119.2. • 90% of IQ scores are below 119.2.

  9. 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.

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

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