## 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**?

- What percentage of FPD Rates are less than the rate for

## 1 Comment

[…] Standard Normal Probabilities […]