2.5 normal distribution swbat calculate areas under a standard normal curve in writing by converting...
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2.5 Normal Distribution SWBAT calculate areas under a
standard normal curve in writing by converting between values and z-scores using a GCD or Table
Warm Up:
Pg 81 Exercise 84.
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Why Normal Distributions?
It tells how variability in repeated measurements often behave
It tells you how variability in populations often behave
Its tells you how means computed from random sample behave
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2.5 The Normal DistributionThe Standard Normal Distribution
Normal Distribution with a mean of 0 and SD of 1
Total area under the curve = 100% Standard Normal Distributions are
symmetrical Variable along the horizontal axis is
the z-score To find area or z-score, can use table
(pg 824-825) or calculator
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Pg 85 D28
For the standard normal distribution: a) what is the median? b) what is the lower quartile? c) what z-score falls at the 95th
percentile? d) what is the IQR
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2.5 The Normal DistributionThe Standard Normal Distribution
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2.5 The Normal DistributionStandard Units Any normal distribution can be re-
centered and re-scaled to become a standard normal distribution.
Formula:
x meanz
SD
Calculator usage: NORMALCDF, INV NORM
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2.5 The Normal DistributionSolving Problems
Always draw a picture! Worth pts Shade the part of the normal curve
you are trying to find If you are looking for a percentage,
you need a z-score (maybe even 2!) If you are looking for another value,
you will still need the z-score. Solve for the unknown.
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2.5 The Normal DistributionCentral Intervals – See Handout
68% of the values lie with 1 SD of the mean
95% of the values lie within 2 SD of the mean
99.7% of the values lie within 3 SD of the mean
90% of the values lie within 1.645 SD of the mean
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Pg 92 D31
Use Table A to verify that 99.7% of the values in a distribution lie within three standard deviations of the mean.
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Problems
Practice for Normal Distribution WS Pg 92 P32-39
Homework:
Pg 93-94 E:59, 61, 63, 64, 67, 69, 71