top of page

Normal Distributions: Finding Values from Areas (Lesson 2.6)

Chapter 2 - Day 7

Learning Targets
  • Find the value that corresponds to a given percentile in a normal distribution.
  • Find the mean or standard deviation of a normal distribution given the value of a percentile.
Activity: Will Marty Make it Back to the Future? Part 2

Experience First

Before starting this lesson, it might be helpful to remind students how to use Table A. Remind them that along the left column of Table A is the z-scores, while all the other values in Table A are areas (to the left!).


Be ready with the following questions to ask students while they are working through page 1 of the Activity.

“Are you given a value or given an area?”

“What is the unknown quantity that you are trying to find?”


The most common student error for question 2 is for students to look for a z-score of 0.85 in Table A. Remind them that the 0.85 is an area, so we are looking for an area as close to 0.85 as we can get (this happens at z = 1.04).

Formalize Later

In this lesson and the previous lesson, we do not show students how to use a calculator or an applet to do normal distribution calculations. We want them to work the homework problems without this knowledge. Tomorrow students will have a practice day for normal distribution calculations and at the end of the practice, we will make them aware of the Normal Distribution applet. While we acknowledge that technology is much faster, we believe that understanding the meaning of a z-score and how it relates to area under a normal curve is critical for student success when we get to statistical inference. For more explanation, here is why we bother with z-scores and Table A.

bottom of page