Lesson 8: Standard Normal Probabilities
October 4, 2015
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?