Lesson 8: Standard Normal Probabilities

October 4, 2015 at 11:21 pm  •  Posted in f15-busad265 by  •  1 Comment

Mon, Oct 5



  • Find probabilities for Z with the Z-Table
  • 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 the Z-Scores in the Z-Table to find corresponding probabilities
    • 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


  • Use the steps above to answer the following questions.
  • Assume a Standard Normal Distribution of men’s heights with mean = 69.4 and std dev = 4.7
    • What percentage of men are less than 64 inches tall?  p(X<64)=?
    • What percentage of men are more than 76 inches tall? p(X>76)=?
    • What percentage of men are between 68 and 72 inches? p(a<X<b)=?


  • Use the Foreign Per Diem (FPD) Rate data from Lesson 7 to answer the following questions.
    • What percentage of FPD Rates are less than the rate for Mexico City?
    • What percentage of FPD Rates are more than the rate for Moscow?
    • What percentage of FPD Rates are between New Delhi and Beijing?


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