5.3. Connecting the Standard Deviation and Normal Distribution http://www.ck12.org
5.3 Connecting the Standard Deviation and Normal Distribution
Learning Objectives
- Represent the standard deviation of a normal distribution on the bell curve.
- Use the percentages associated with normal distribution to solve problems.
Introduction
In the problem presented in lesson one, regarding your test mark, your teacher told you that the class marks were
normally distributed. In the previous lesson you calculated the standard deviation of the marks by using the TI83
calculator. Later in this lesson, you will be able to represent the value of the standard deviation as it relates to a
normal distribution curve.
You have already learned that 68% of the data lies within one standard deviation of the mean, 95% of the data lies
within two standard deviations of the mean and 99.7% of the data lies within three standard deviations of the mean.
To accommodate these percentages, there are defined values in each of the regions to the left and to the right of the
mean.
These percentages are used to answer real world problems when both the mean and the standard deviation of a data
set are known.
Example 1:
The lifetimes of a certain type of calculator battery are normally distributed. The mean life is 400 hours, and the
standard deviation is 50 hours. For a group of 5000 batteries, how many are expected to last
a) between 350 hours and 450 hours?
b) more than 300 hours?
c) less than 300 hours?
Solution:
a) 68% of the batteries lasted between 350 hours and 450 hours. This means that( 5000 ×. 68 = 3400 )3400 batteries
are expected to last between 350 and 450 hours.