Normal Distribution and The Empirical Rule Get out

Normal Distribution and The Empirical Rule Get out your notes. Open Note Unit 3 Test on Friday.

Learning Objectives • Be able to recognize a normal distribution curve • Be able to use the Empirical Rule to predict measurements that are normally distributed. • Apply the Empirical Rule to predicting the quality of measured blocks.

Review 1. How can you determine if it is a Normal Distribution? 2. Bell Shaped Curve 3. Peaks at the mean 4. Curve decreases on both sides away from the mean 5. Curve is symmetric. Looks the same on both side.

Empirical Rule • Applies to normal distributions • Almost all data will fall within three standard deviations of the mean

Empirical Rule If the data are normally distributed: • 68% of the observations fall within 1 standard deviation of the mean. • 95% of the observations fall within 2 standard deviations of the mean. • 99. 7% of the observations fall within 3 standard deviations of the mean.

Empirical Rule Example Data from a sample of a larger population

68 % 0. 08 + 1. 77 = 1. 88 0. 08 + - 1. 77 = -1. 69 Normal Distribution s s -1. 77 +1. 77 Data Elements

0. 08 + 3. 54 = 3. 62 0. 08 + -3. 54 = - 3. 46 Normal Distribution 95 % 2 s - 3. 54 2 s + 3. 54 Data Elements

Example

Review • What is the Empirical Rule? • Given a mean value of 10 with a standard deviation of 2: – What range of values would 68% of the data fall in? – What range of values would 95% of the data fall in? – What range of values would 99. 7% of the data fall in? • Can you apply the Empirical rule to all sets of data?

Tasks Friday’s Test is Open Notes (Your notebooks), not internet/cell phone/Smith’s Website • Complete Worksheet 3. 3 (the cube measuring worksheet) • When finished you can check past Power. Points and add information to your notes to be used on Friday’s exam. • Test Topics – US/SI Measurements – Unit Conversions – Using Dial Calipers – Statistics: Mean, Median, Mode, Standard Deviation, Histogram – Using Excel to calculate statistics – Normal Curves – The Empirical Rule • Practice Test