Lecture 21 Section – Tue, Oct 10, 2006

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Presentation transcript:

Lecture 21 Section 6.3.1 – 6.3.2 Tue, Oct 10, 2006 Normal Percentiles Lecture 21 Section 6.3.1 – 6.3.2 Tue, Oct 10, 2006

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

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.

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.

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%.

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%.

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.

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.

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.

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