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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?