once again, my blog site is you should visit this site to get notes and assignments, check
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Once again, my blog site is www.mathwithdillon.weebly.com
You should visit this site to get notes and assignments, check HW and WS, and check the calendar for assessment dates.
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Come see me if you don’t understand a concept.
You should bring your worked homework problems so I can see what your mistake is.
You have to attempt homework problems before I can help you. I don’t know how to help you unless I see some work from you.
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Accel Math IIIUnit #1: Data Analysis
Lesson #8: Normal Distribution
EQ: What are the characteristics of a normal distribution and how is probability calculated using this type of distribution?
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Recall: Three Types of Distributions
Binomial Normal Geometric
Normal Distributions --- created from continuous random variables
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Characteristics of a Normal Distribution:1. Symmetric, Bell-Shaped Curve and Uni-modal.
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2. Mean, Median, Mode are equal and located at the middle of the distribution. Symmetric about the mean. Not skew.
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3. The curve is continuous, no gaps or holes. The curve never touches or crosses the x-axis.4.The total area under the curve equals
1.Recall: Empirical Rule
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Normal Distribution --- each has its own mean and standard deviation.
What are µ and σ in this normal distribution ?50 10
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Standard Normal Distribution --- mean is always 0 and standard deviation is always 1
STANDARDIZE
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z-score --- the number of standard deviations above or below the mean
z = observed – mean or z = X - µ standard deviation σ
Correlates to areaunder the curve.
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Ex. In a study of bone brittleness, the ages of people at the onset of osteoporosis followed a normal distribution with a mean age of 71 and a standard deviation of 2.8 years. What z-score would an age of 65 represent in this study?
62.6 65.4 68.2 71 73.8 76.6 79.4
| | | | | || | | | | |-3 -2 -1 0 1 2 3
14.28.27165
z
| 65
| -2.14
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Using Table A to Finding the Area under A Standard Normal Curve
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Ex. Find the area under the curve to the left of z = -2.18.
| -2.18
%46.10146.0)18.2( zP
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Ex. Find the area under the curve to the left of z = 1.35.
| 1.35
%15.919115.0)35.1( zP
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Ex. Find the area under the curve to the right of z = 0.75.
| .75
%66.222266.07734.01)75.0( zP
WHY??
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Ex Find the area under the curve between z = -1.36 and z = 0.42.
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Ex. Find the area under the curve between z = 1.60 and z = 3.3.
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In Class Practice Worksheet: Area Under the Standard
Normal Curve#1 - 11
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What about finding a z-score when given area under the curve?Ex. Determine the z-score that would
give this area under the curve.
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Ex. Determine the z-score that would give this area under the curve.
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Ex. Determine the z-score that would give this area under the curve.
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In Class Practice Worksheet: Area Under the Standard
Normal Curve#12
Practice Worksheet Calculating Area Using z-scores
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Quiz 2 --- 30 minutes
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Using the Graphing Calculator with Normal Distributions
Command and Arguments: I. When given a z-score, you are
looking for area under the curve.
normalcdf(low bound, high bound)
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Ex. Find the area under the curve to the left of z = 1.35.
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Ex Find the area under the curve between z = -1.36 and z = 0.42.
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Assignment: Example Handout: Area Under
the Standard Normal Curve #1 – 11
Go back and rework these using the calculator function.
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II. When given area, you’re looking for a z-score.
Use invnorm function under distributions.invnorm(% to the left)
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***Remember invnorm and normcdf are calculator jargon
Do not write these functions on assessments as “work”.Assignment: Redo WS Calculating Area
Using z-scores