The Empirical Rule and Assessing Normality (Lesson 2.4)
Chapter 2 - Day 5
Use the empirical rule to estimate the proportion of values in a specified interval in a normal distribution.
Use the empirical rule to estimate the value that corresponds to a given percentile in a normal distribution.
Use graphical and numerical evidence to determine if a distribution of quantitative data is approximately normal.
The context for this lesson comes from the stopwatch task in the previous lesson. Students will need a laptop or their phone to be able to access the Normal Distributions applet at www.statsmedic.com/applets.
Notice that this lesson has a STOP sign at question 6. This indicates to students that their groups should work through question 5, and then stop to wait for the full class debrief of the first 5 questions of the activity before moving to question 6. When you finish the debrief of 1-5 (where you will introduce the empirical rule), inform students that they cannot use the applet for questions 6-8 (they have to use the empirical rule!)
Students might have seen the 0.15, 2.35, 13.5, 34 rule in their Algebra 2 class, which gives the percent of values in each chunk on the left side of the normal distribution. Of course this is consistent with the empirical rule.
Note that the 3rd Learning Target about assessing normality is not covered in the Activity. Students will get practice with this Learning Target in the first 3 questions of the Check Your Understanding.
As stated in the previous lesson, student understanding of Normal distributions is critical for their success in this course. Today, we are trying to get them thinking and reasoning about how values are distributed in a normal distribution. In the next two lessons, we will get much more formal about calculating areas in a normal distribution.