2.2 Normal Distributions Normal Curves: symmetric, single-peaked, bell- shaped. and median are the same. Size of the will affect the spread of the normal curve.

Example Scores on the SAT verbal test in recent years follow approximately the N (505, 110) distribution. How high must a student score in order to place in the top 10% of all students taking the SAT? 1. State the problem and draw a picture. Shade the area we’re looking for. 2. Find the Z score with the table 3. Convert to raw score.

Assessing Normality Method 1: Construct a histogram, see if graph is approximately bell-shaped and symmetric. Median and Mean should be close. Then mark off the -2, -1, +1, +2 SD points and check the 68-95-99.7 rule.

Normal Probability Plot Method 2: Construct Normal Probability Plot 1. Arrange the observed data values from smallest to largest. Record what percentile of the data each value occupies (example, the smallest observation in a set of 20 is at the 5% point, the second is at 10% etc.) Use Table A to find the Z’s at these same percentiles (example -1.645 is @ 5%, -1.28 is @10% Plot each data point against the corresponding Z (x- values on the horizontal axis, z-scores on the vertical axis is what I do, either is fine)

rkgnt Normal w/Outliers Right Skew Normal Interpretation: draw your X = Y line with a straight edge- points shouldn’t vary too much

Constructing Probability Plot on Calculator Students in Mr. Pryor’s stats class X values on horizontal axis 79 81 80 77 73 83 74 93 78 75 67 86 90 85 89 84 82 72