Download Normal Distributions Curves that are symmetric, single

Normal Distributions
Curves that are symmetric, single-peaked, and bell-shaped are often called normal curves and describe
normal distributions. All normal distributions have the same overall shape. They may be "taller" or
more spread out, but the idea is the same. The "control factors" are the mean µ and the standard
deviation σ. Changing only µ will move the curve along the horizontal axis. The standard deviation σ
controls the spread of the distribution. Remember that a large σ implies that the data is spread out.
You can locate the mean by finding the middle of the distribution. Because it is symmetric, the mean
is at the peak. The standard deviation can be found by locating the points where the graph changes
curvature (inflection points). These points are located a distance σ from the mean.
A most handy rule of thumb for normal distributions is the 68-95-99.7 rule.
The 68-95-99.7 Rule
In a normal distribution with mean µ and standard deviation σ,
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68% of the observations are within σ of the mean µ.
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95% of the observations are within 2 σ of the mean µ.
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99.7% of the observations are within 3 σ of the mean µ.
Insert Example 2.2 from the Yates text.
Since we use normal distributions often, we use this notation. N (µ,σ).
Why use normal distributions?
1. They are occur frequently in large data sets (all SAT scores), repeated measurements of the same
quantity, and in biological populations (lengths of roaches).
2. They are often good approximations to chance outcomes (like coin flipping).
3. We can apply things we learn in studying normal distributions to other distributions.
However, NOT ALL DATA are normal or even close to normal. Salaries, for instance, are generally
right skewed. Nonnormal data are common and often interesting.