## Lesson 10: Solving Normal Curve Problems

September 21, 2016

Wed, Sep 21

Review:

- Standard Normal Calculations with Z-Scores
- Exam 1 Part 1

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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