practice_normal

# practice_normal - Given a population with µ = 30 and σ =...

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Given a population with μ = 30 and σ = 5, 1. What proportion of the data are higher than 32.5? 2. At what value is the 25th percentile? 3. What percent of the data are higher than 24? 4. What value is exactly 60 percent of the data lower then? 5. What percent of the data falls between values of 32 and 35? 6. What value is below exactly 10 percent of the data?

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Given a population with μ = 30 and σ = 5, 1. What proportion of the data are higher than 32.5? Convert to z-value: z = (x-μ)/ σ = (32.5-30)/5 = .5 ? x: 30 32.5 z: 0 .5 Either: For z = .5 in column A, lookup the corresponding area from column C: .3085 Or: For z = .5 in column A, lookup the corresponding area from column B: .1915 .5 - .1915 = .3085 2. At what value is the 25th percentile? .25 x: ? 30 z: ? 0 For an area of .25in column C, lookup corresponding z score in column A: ~.67 Take negative, -.67 Convert z-score to data value, x = (z)( σ ) + μ = (-.67)(5) + 30 = 26.65
3. What percent of the data are higher than 24? Convert to z-value: z = (x-μ)/ σ = (24-30)/5 = -1.2 ? x: 24 30 z: -1.2 0 Take absolute value of -1.2=1.2 Either: For z = 1.2 in column A, lookup the corresponding area from column C: .1151 1 - .1151 =.8849 (.8849)100=88.49% Or: For z = 1.2 in column A, lookup the corresponding area from column B: .3849 .5 + .3849 =.8849 (.8849)100=88.49% 4. What value is exactly 60 percent of the data lower then? .60 x: 30 ? z: 0 ? Calculate the just the area above the mean: .60 - .5 = .1 For an area of .1 in column B, lookup corresponding z score in column A: .2 Convert z-score to data value, x = (z)( σ ) + μ = (.25)(5) + 30 = 31.25

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5. What percent of the data falls between values of 32 and 35? Convert both to z-value: z = (x 1 -μ)/ σ = (32-30)/5 = .4 z = (x 2 -μ)/ σ = (35-30)/5 = 1 ? x:
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## This note was uploaded on 02/06/2010 for the course PSYC psych 60 taught by Professor Federico during the Fall '09 term at UCSD.

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practice_normal - Given a population with µ = 30 and σ =...

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