Normal Percentiles Lecture 21 Section 6 3 1

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Normal Percentiles Lecture 21 Section 6. 3. 1 – 6. 3. 2 Tue, Feb

Normal Percentiles Lecture 21 Section 6. 3. 1 – 6. 3. 2 Tue, Feb 28, 2006

Standard Normal Percentiles Given a value of Z, we know how to find the

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 n The problem of finding a percentile is exactly the reverse: n n Given the area to the left of a value of Z, find that value of Z? Area to the left Value of z n That is, given the percentage, find the percentile.

Standard Normal Percentiles What is the 90 th percentile of Z? n That is,

Standard Normal Percentiles What is the 90 th percentile of Z? n That is, find the value of Z such that the area to the left is 0. 9000. n Look up 0. 9000 as an entry in the standard normal table. Read the value of Z. n Use the inv. Norm function on the TI-83. n

Standard Normal Percentiles on the TI-83 n To find a standard normal percentile on

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

Practice n Use the TI-83 to find the following percentiles. Find the 99 th

Practice n Use the TI-83 to find the following percentiles. Find the 99 th percentile of Z. n Find the 1 st percentile of Z. n Find Q 1 and Q 3 of Z. n What value of Z cuts off the top 20%? n What values of Z determine the middle 30%? n

The Standard Normal Table n Use the normal table to find the following percentiles.

The Standard Normal Table n Use the normal table to find the following percentiles. Find the 99 th percentile of Z. n Find the 1 st percentile of Z. n Find Q 1 and Q 3 of Z. n What value of Z cuts off the top 20%? n What values of Z determine the middle 30%? n

Normal Percentiles n To find a percentile of a variable X that is N(

Normal Percentiles n To find a percentile of a variable X that is N( , ), Find the percentile for Z. n Use the equation X = + Z to find X. n

Example Let X be N(30, 5). n Find the 90 th percentile of X.

Example Let X be N(30, 5). n Find the 90 th percentile of X. n The 90 th percentile of Z is 1. 64. n Therefore, X = 30 + (1. 28)(5) = 36. 4. n n 90% of the values of X are below 36. 4.

TI-83 – Normal Percentiles Use the TI-83 to find the standard normal percentile and

TI-83 – Normal Percentiles Use the TI-83 to find the standard normal percentile and use the equation X = + Z. n Or, use inv. Norm and specify and . n n inv. Norm(0. 90, 30, 5) = 36. 4.

Practice Find the 95 th percentile of IQ scores, using N(100, 15). n Find

Practice Find the 95 th percentile of IQ scores, using N(100, 15). n Find the 80 th percentile of test scores, using N(75, 10). n

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