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```AP Statistics – Chapter 6, The Standard Deviation as a
Ruler and the Normal Model (Day 3)
Name: _______________________________
Date: _______________
“If someone tells you you’re ‘one in a million’, they must really admire your z-score.”
I.
Warm-up Refer back to Day 2 Notes, example (c).
II.
z-scores being Normal or Unusual
How extreme a z-score is can be “modeled” by a normal model, or normal distribution. Typically
a bell-shaped curve because the distributions are unimodal and roughly symmetric. The book uses
𝑁(𝜇, σ), but really it is nothing more than:
BE CAREFUL!! The mean and standard deviation, in this case, are not summaries of data. They
are numbers to help specify the model.
*ActivStats (z-scores being normal)
Be sure to check for in data: “The Nearly Normal Condition”
III.
The 68-95-99.7 Rule
If a distribution is known to be normal, then in observing the bell-shaped curve, three important
things will happen every time:
68% of the data will ______________________________________________________________
95% of the data will ______________________________________________________________
99.7% (or almost all) of the data will _________________________________________________
*ActivStats (68-95-99.7 Rule)
IV.
Examples (use the back of this page if you need more room)
(a) Just Checking #4, page 109
(b) Just Checking #5, page 109, a) and b) only
(c) The SAT has three parts, and each part has a distribution that is roughly unimodal and
symmetric and is designed to have an overall mean of about 500 and a standard deviation of
100 for all test takers.* Supposed you earned 600 on one part of your SAT. Where do you
stand among all students who took that test?
```
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