Download Chapter 2 Assignments

Chapter 2 Assignments
AP #8
Measures of Relative Standing: percentiles and z-scores; Chebyshev’s Inequality
• Reading: Introduction and Section 2.1, pages 116-122. Please take notes for credit.
Cartoon Guide to Statistics, pages 7-26
• Exercise: 2.2, 2.3, 2.4, 2.7, 2.8
Note: Read the materials carefully. You are in an Advanced Placement course.
Reading…and understanding what you read is important.
•
Items for Reflection:
You are in Section 2.1.
Cartoon Guide to Statistics is an easy -to –read-and-understand book. There is a
lot of good stuff mixed in among the cartoon figures. The pages you will be reading
represent a review of what we have done to date, plus a very brief introduction (pages
24-27) to some new thoughts that will be very important to us. Take the appropriate
notes you deem important from both the text reading and the cartoon reading. I will
expect to see some notes for five points credit towards homework.
AP #9
Density Curves; Normal Distributions and the 68-95-99.7 Rule
• Reading: pp. 123-137
• Exercises: 2.9, 2.10, 2.12, 2.14(There is a lot that can be learned from this
simulation.), 2.23, 2.24, 2.25
AP #10
Standard Normal Curve and table; Nonstandard Normal Curves and calculation
• Reading: pp. 139-147
• Exercises: 2.29, 2.32, 2.33, 2.35
• Items for Reflection:
It is important to realize that you can standardize any set of numerical scores.
Such a set will have a mean and a standard deviation, so you can calculate a zvalue for each score by subtracting the mean, and then dividing by the
standard deviation. This can be useful, since the z-scores represent the
number of standard deviations to the left or to the right of the mean.
However, just standardizing a set of scores does not produce a normal
distribution of z-scores. If your initial scores are normal, then the
standardized scores will also be normally distributed. A common error
involves thinking that standardizing scores automatically produces a normal
distribution. Don’t make this very careless mistake.
AP #11
Assessing Normality: Normal Probability Plots; other graphical and numerical
methods
• Reading: pp. 148-159
• Exercises: 2.36, 2.37, 2.38, 2.39, 2.50
• Items for Reflection:
Please pay attention to exercise 2.39. Remember the Who, What, Why,
When, Where, How, and by Whom? in the Data Analysis Toolbox. I
will be looking for complete, well-constructed sentences for this exercise.
• Items for Reflection:
You are in Section 2.2.
You should be able to understand, and read, the normal distribution table.
The TI-83 is also quite helpful. Here is a simple example. Suppose a
normal distribution has a mean = 73.2 and standard deviation = 4, and that
we want to know the percentage of scores between 72 and 76.
One approach: normalcdf(72,76,73.2,4) = .3759477798, or about 37.6%.
Another approach: z score for 72 = (72 –73.2)/4 = -0.3 and z score for 76
= (76 – 73.2)/4 = 0.7. We can then calculate normalcdf(-.3,.7,0,1) =
.3759477798 or about 37.6%.
Make sure you can get this result using the normal distribution table.
AP #12
Practice Problems with Density Curves
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Reading: pp. 161 (Chapter Review) – 167 (Tech Toolboxes)
Exercises: 2.43, 2.44,2.45, 2.48, 2.54, 2.58, 2.59
Items for Reflection
Be sure to check out the Technology Toolboxes. You want to use what works for you.
Although you can use your calculators on the AP Exam you do want to avoid “calculator
speak”. For example, normalcdf(125, 1E99, 100, 15) translates, for you as a writer on the
exam, into “I am finding the area under a normal curve from 125 points and above that
has a mean of 100 and a standard deviation of 15)”.