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Normal Percentiles

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:

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Normal Percentiles

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

  2. 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.

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

  4. Practice • Find the 99th percentile of Z. • Find the 1st percentile of Z. • Find the 50th 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%?

  5. 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.

  6. 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.

  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 • 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.

  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(0.95, 30, 5) = 38.2.

  10. Assignment • Page 341: Exercises 6, 8, 15, 16, 19, 21. • Page 361: Exercises 47, 49, 53, 57, 58, 59, 68, 78.

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