Lecture 21 Section – Fri, Feb 22, 2008

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

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. On the 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 (Item #3). 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%.

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 1.282. 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 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.