Mr. Rogers - AP Statistics Objectives
Syllabus 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
1 Distributions 2 N-Distribution 3 Regression 4 NL Regression 5 Data
Unit Plan Practice Test

AP Statistics Standards

I. Exploring Data:  (continued).

II. Anticipating Patterns:

C. The normal distribution

  1. Properties of the normal distribution

  2. Using tables of the normal distribution

  3. The normal distribution as a model for measurements

Objectives
Essential Question: Does all data fit a bell curve?

The Normal Distribution

  1. Define density curve.
    • Models the a distribution
    • Above horizontal axis
    • Area under it = 1
    • Area under part of the curve = probability 
  1. Describe the normal distribution.
  • Symetrical
  • Bell Shaped
  • Range negative infinity to positive infinity
  1. Be as one with the 68-95-99.7 Rule for normal distributions. Note: in the 1st part of the test for this chapter, you will not be permitted to use calculators or tables. The entire test will be based on the above rule.
  1. Be as one with the 0-75-89 Rule for any distribution. Note: this is the worst case situation for any distr.
Chebyshev's Rule: p = (1 - 1/k^2)
  1. State where the 2 inflection points fall on a normal distribution. This will help you draw the norm. distr.
  2. Correctly use N(mean, sigma) notation.
  3. State the effects on a normal distribution of increasing standard deviation.
  4. According to the normal distribution, what is the probability of obtaining an exact value for a data point.

Homefun: prob. 2.3, 2.5, 2.7, 2.9

 

Activities
 
 
Lesson 1
Key Concept: What is a normal distribution?
Purpose: Lay the foundation for using the normal distribution.

Interactive Discussion: Objectives. Explain why the 68-95-99.7 Rule is critical for developing "normal distribution intuition".

Seat Work: Use the empirical rule to find various areas under the n-distribution.

 

 

Essential Question: What does the area under the "bell curve" mean?

Finding Areas Under the Normal Distribution

  1. Calculate z-scores.
    z = distance from mean in std dev units
  1. Estimate the probability of obtaining a range of values by using the normal distribution. (find the area under the curve)

Probability = area under curve

  1. Find z-scores corresponding to Q1 &Q3 of a box and whiskers plot for normally distributed data.
  2. Using a normal distribution, estimate a critical value given the probability of finding a value as extreme or more extreme (a tail area).
  3. Judge the normality of a distribution by examining histograms, stem plots, dot plots, or box and whiskers plots.
    • Bell shaped
    • Symmetrical
    • 68-95-99.7 Rule
  1. Judge the normality of a distribution using a normal quantile plot on a TI-83.

Homefun: prob. 2.12, 2.13, 2.17

  1. Work quality control reject rate problems.
  2. Convert a normal distribution into a cumulative frequency plot.
Lesson 2
Key Concept: Area under the normal distribution and how it relates to a box and whiskers plot.

 

Purpose: Understand when a data set is normally distributed.

Interactive Discussion: Objectives

2-person teams: Derive an equation for the z-score

Seat Work: Find the area under n-distribution using tables and the TI-83 calculator.

2-person teams:

  • Derive the z-scores of Q1, Q2, LL, UL
  • Draw a box and whiskers diagram of an n-distribution