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.

A distribution of all possible values of a variable with an indication of the likelihood that each will occur –A probability distribution can be represented by a probability density function Normal Distribution – most commonly used probability distribution Probability Distribution Distribution

“Is the data distribution normal?” 1.Translation: Is the histogram/dot plot bell-shaped? 2.Does the greatest frequency of the data values occur at about the mean value? 3.Does the curve decrease on both sides away from the mean? 4.Is the curve symmetric about the mean? Normal Distribution Quick Check Noteworthy

Frequency Data Elements Bell shaped curve Normal Distribution? Distribution

Frequency Data Elements Mean Value Normal Distribution? Distribution Does the greatest frequency of the data values occur at about the mean value?

Frequency Data Elements Mean Value Normal Distribution ? Distribution Does the curve decrease on both sides away from the mean?

Frequency Data Elements Mean Value Normal Distribution? Is the curve symmetric about the mean?

What if the data is not symmetric? Histogram Interpretation: Skewed (Non-Normal) Right

What if the data is not symmetric? A normal distribution is a reasonable assumption.

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.

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.

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

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 If the data are normally distributed:

Empirical Rule Example Data from a sample of a larger population

Data Elements Normal Distribution s s = = %

Data Elements Normal Distribution 2s s = = %

Your Turn Revisit the data you collected during the Fling Machine Instant Challenge. Assume that you repeated launch cotton balls with your device. Using the mean and sample standard deviation of your data: –Predict the range of travel distances within which 68% of cotton balls would fall –Predict the range of travel distances within which 95% of cotton balls would fall

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 Complete Worksheet 3.3 (the cube measuring worksheet) When finished you can check past PowerPoints 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 Friday’s Test is Open Notes (Your notebooks), not internet/cell phone/Smith’s Website