The mathematical purpose of the lesson is to find areas under a normal curve and interpret the area as a proportion of values in the interval using a variety of different contexts. The work of this lesson connects to previous work because students applied the concepts of mean and standard deviation to data modeled using a normal distribution and were introduced to the area under a normal curve. The work of this lesson connects to upcoming work because students will compare models to data collected from simulations. When students find the areas under a normal curve and interpret the proportion of values in certain intervals for a given context, they are looking for and making use of structure (MP7).
Students can perform the work in this lesson using a table and \(z\)scores; however, the activities in this lesson work best when each student has access to technology because it may take too long to do otherwise. If students are using technology to find areas under normal curves, technology will give the exact area without needing calculations that would be required when using the tables.
Lesson overview
 7.1 Warmup: Find the Areas (5 minutes)
 7.2 Activity: Life of Lights (15 minutes)

7.3 Optional Activity: Waiting for a Waiter (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 7.4 Cooldown: Brown Bear, What Do You See? (5 minutes)
Learning goals:
 Determine areas under a normal curve.
 Interpret (orally and in writing) the proportion of values in certain intervals under a normal curve in a variety of different contexts.
Learning goals (student facing):
 Let’s use the normal distribution to estimate the proportion of data values falling within given intervals.
Learning targets (student facing):
 I can use the mean and standard deviation of a normally distributed data set to estimate intervals when given a proportion.
 I can use the mean and standard deviation of a normally distributed data set to estimate proportions.
Required materials:
 Statistical technology
Required preparation:

Be prepared to display a GeoGebra applet for all to see during the activity Life of Lights.
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