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Chapter 7
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Characteristics of normal probability distribution
-Bell shaped with single peak at center of distribution.
- Symmetrical about mean
- Asymptotic- Curve gets closer and closer to x axis, but never touches
- Location of normal distribution determined by mean
- Dispersion or spread determined by standard deviation
- Mean, median, mode are equal
- Total area under curve is 1.00. Half are to both sides of center point.
Normal distribution pic
Z distribution
a normally distributed set of specially scaled values whose mean is always equal to zero and whose standard deviation must equal 1.00
Z value formula for single data
Review examples on 7-8 through 7-16
...
The Empirical Rule and pic
in a bell-shaped distribution, 68% within 1 standard deviation, 95% within 2 standard deviations, 99.7% within 3 standard deviations
Relationship between normal percentile and percentile of z is...
x= mean + (Standard deviation)(z)
Alternative method to finding z values
2nd distribution, normalcdf( smaller, larger)
How to find percentile
1. 2nd distribution, invnormal (percentile in decimal form)
2. That spits out z value
3. Use the formula x= mean + (standarddev)(z)
Z score practice problems
...
A normally distributed random variable has any value between negative infinity and positive infinity
...
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