Lesson 10: Solving Normal Curve Problems

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September 21, 2016 at 2:00 am  •  Posted in f16-busad265 by  •  1 Comment

Wed, Sep 21

Review:

Presentation:

  • Find probabilities for Z-Scores with the Z-Table (use this link or back page of textbook)
  • Normal Distribution Probability Problems: 3 Types
    • p(X<a) = “Less Than”
    • p(X>b) = “Greater Than”
    • p(a<X<b) = “Between” (between 2 values)
  • Steps to finding Standard Normal Probabilities
    • Draw a picture of the distribution
    • Convert given values (a, b) to Z-Scores and locate on the horizontal axis
    • Look up corresponding probabilities in the Z-Table
    • Decide if it’s a “Less Than”, “Greater Than” or “Between” problem
      • If “Less Than”, shade under the curve to the left of Z-Score; the Z-Table probability you found is the answer.
      • If “Greater Than”, shade under the curve to the right of the Z-Score; subtract the Z-Table probability from 1 to find the answer.
      • If “Between”, you will have 2 probabilities from the Z-Table
        • Shade the area under the curve between the two Z-Scores
        • Find the probability for the larger value (further to the right)
        • Find the probability for the smaller value (further to the left)
        • Subtract the smaller from the larger to find the “Between” probability
  • Inverse Normal Curve calculations
    • Z = (x – xbar)/s
    • x = xbar + Z * s
    • xbar = mean
    • s = standard deviation
  • Examples
    • Step through examples 1.29, 1.30 and 1.31 on pp. 65-66
    • Step through example 1.32 on pp. 67-68

Activity:

  • Use the steps above to answer the “Use Your Knowledge” questions
    • 1.103 and 1.104 on p. 66
    • 1.105 and 1.106 on p. 68

Assignment:

  • Read pp. 64-68
  • Work on Exam 1 Part 1 Take Home

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