Lesson 8: Normal Curves

September 13, 2016

Wed, Sep 14

Review:

• Exam 1 will be on Wed, Sep 28
• Variance and Standard Deviation
• Why do we divide by n – 1?
  • http://nebula.deanza.edu/~bloom/math10/m10divideby_nminus1.pdf
  • https://en.wikipedia.org/wiki/Bessel%27s_correction#Proof_of_correctness_-_Alternate_3
  • https://economictheoryblog.com/2015/04/01/unbiased-estimator-of-sample-variance/

Presentation:

• Density Curves
  • Height of curve indicates proportion of values
  • Area under the curve = 1.0
    • Any sub-area under the curve is then a proportion (% of values)
• Normal Curves
  • A special case of density curves
  • Bell shaped and symmetrical
  • Mean and Standard deviation
  • 68 – 95 – 99.7 Rule
  • Video

Activity:

• Problem 1.
  • Height of 4-year-old boys is approximately normally distributed with mean 40 inches and standard deviation 1.5 inches.
    • Draw a normal density curve and label the mean on the horizontal axis.
    • Also mark points on the horizontal axis one standard deviation on either side of the mean.
• Problem 2.
  • IQ scores are normally distributed with mean 100 and standard deviation 15. Scores from 90 to 110 represent normal or average intelligence. Scores above 120 represent superior intelligence.
    • Draw a normal density curve for IQ scores.
    • Label the mean and one standard deviation on either side of the mean.
    • Shade the area under your normal curve that represents the proportion of people with normal intelligence.
    • Then shade, in a different way, the area representing the proportion of people with superior intelligence.

Assignment:

• Read pp. 53-61 Density Curves and Normal Distributions
• Complete the Use Your Knowledge questions 1.99 and 1.100 on pp. 60-61