STAT 1301 Chapter 5(a) The Normal Curve

Histogram Comparison of 2 Tests

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

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

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

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

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

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