Lesson 9: Standard Normal Calculations with Z-Scores

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September 19, 2016 at 4:00 am  •  Posted in f16-busad265 by  •  0 Comments

Mon, Sep 19

Review:

  • Normal Curves
  • Exam 1
    • Part 1 Instructions
    • Review for Exam 1 on Mon, Sep 26
    • Exam 1 Part 2 in-class exam on Wed, Sep 28

Presentation:

  • Standard Normal Distribution
    • Mean = 0
    • Standard Deviation = 1
  • Z-Scores
    • (x – mean)/std dev
    • Example (p. 61)
      • Young women heights normally distributed
      • Mean = 64.5 in
      • Standard Deviation = 2.5 in
      • Z-Score for woman 68 inches tall
        • Z = (68 – 64.5)/2.5 = 1.4
      • Z-Score for woman 60 inches tall
        • Z = (60 – 64.5)/2.5 = -1.8
  • Normal Curve Calculations with Z-Scores
    • % Greater than
      • z > 0
      • z > 1
    • % Less than
      • z < 0
      • z < 1
    • % Between
      • 0 < z < 1
      • 1 < z < 2
  • Normal Calculations video

Activity:

1. The distribution of heights of young women (18 – 24 years old) is approximately normal with mean = 64.5 inches and standard deviation = 2.5 inches.

  • Draw a normal curve with a horizontal axis. Label mean.
  • What is the z-score for a 20-year-old woman who is 6 feet tall? Label point.
  • Between what two values do the heights of the central 95% of young women lie? Shade this area.
  • What % of young women are more than two standard deviations taller than the mean?

2. There are two national college-entrance examinations, the SAT and the American College Testing program (ACT). Scores on individual SAT exams are approximately normal with mean = 500 and standard deviation = 100. Scores on the ACT exams are approximately normal with mean = 18 and standard deviation = 6.

  • Julie’s SAT Math score is 630. John’s ACT Math score is 22. Calculate the standardized Z-scores for both.
  • Assuming that both tests measure the same kind of ability, who has the higher score?
  • What percent of all SAT scores are above 600?

3. Find the percentage of observations from a standard normal distribution that satisfy the following.

  • z < −1
  • z > 2
  • −1 < z < 2

Assignment:

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