Lecture 21 Section – Fri, Oct 15, 2004

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Lecture 21 Section 6.3.1 – 6.3.2 Fri, Oct 15, 2004 Normal Percentiles Lecture 21 Section 6.3.1 – 6.3.2 Fri, Oct 15, 2004

Standard Normal Percentiles Given a value of Z, we know how to find the area to the left of that value of Z. 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? That is, given the percentage, find the percentile.

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. Look up 0.9000 as an entry in the standard normal table. Read the corresponding value of Z. Z = 1.28.

Practice Find the 99th percentile of Z. Find the 1st percentile of Z. Find Q1 and Q3 of Z. What value of Z cuts off the top 20%? What values of Z determine the middle 30%?

Standard Normal Percentiles on the TI-83 To find a standard normal percentile on the TI-83, Press 2nd DISTR. Select invNorm. Enter the percentile as a decimal (area). Press ENTER.

Standard Normal Percentiles on the TI-83 invNorm(0.99) = 2.236. invNorm(0.01) = -2.236. invNorm(0.50) = 0. Q1 = invNorm(0.25) = -0.674. Q3 = invNorm(0.75) = 0.674. invNorm(0.80) = 0.8416. invNorm(0.35) = -0.3853. invNorm(0.65) = 0.3853.

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 Let X be N(30, 5). Find the 95th percentile of X. The 95th percentile of Z is 1.64. Therefore, X = 30 + (1.64)(5) = 38.2. 95% of the values of X are below 38.2.

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(0.95, 30, 5) = 38.2.

Assignment Page 341: Exercises 6, 8, 15, 16, 19, 21.