1. STAT 1301 Chapter 5(a) The Normal Curve

3. Histogram Comparison of 2 Tests

5. The Normal Curve Many histograms of natural data are “bell” shaped
We trade the problem of finding area under bars of a histogram for that of finding area under the normal curve

6. Properties of the Normal Curve
“smooth”: not composed of blocks like a histogram
symmetric : right half is the mirror image of left half.
The total area under the curve is 100%, just like a histogram.
Areas can be found using Normal Tables

7. How to Use Normal Table (A-105)
STEP 1: Convert data value to Standard Units (z-score)
- standard units measure how many SD’s above or below the AVG a given value is
- FORMULA for finding Standard Units: Value - AVG z = SD

9. STEP 2: Look up standard units (Z-score) in Table A-105
- Given a Z-score, the table gives “Area” which is the area under the curve from -Z to Z
- This tells us the % of the distribution with Z-scores between these values

11. In general “ DRAW PICTURE” to determine % (area) for your problem

12. 2-step Procedure
STEP 1: Convert data value to Standard Units (z-score)
Value - AVG z = SD
STEP 2: Find area (%) using normal curve