Lesson 8: Standard Normal Probabilities

October 4, 2015

Mon, Oct 5

Review:

• Normal Distribution
• Z-Scores
• Grading

Presentation:

• 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

Activity:

• 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)=?

Assignment:

• 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?