5.3. Applications of the Normal Distribution http://www.ck12.org
5.3 Applications of the Normal Distribution
Learning Objectives
- Apply the characteristics of the normal distribution to solving problems.
Introduction
The normal distribution is the foundation for statistical inference and will be an essential part of many of those topics
in later chapters. In the meantime, this section will cover some of the types of questions that can be answered using
the properties of a normal distribution. The first examples deal with more theoretical questions that will help you
master basic understandings and computational skills, while the later problems will provide examples with real data,
or at least a real context.
Unknown Value Problems
If you truly understand the relationship between the area under a density curve and the mean, standard deviation,
andz−score, you should be able to solve problems in which you are provided all but one of these values and are
asked to calculate the remaining value. While perhaps not directly practical, it is the thorough understanding of these
calculations that will lead to a high degree of comfort when a more relevant context is provided.
In the last lesson we found the probability, or area under the density curve. What if you are asked to find a value that
gives a particular probability?
Example:
Given a normally distributed random variablexwithμ=35 andσ= 7 .4, what is the value ofxwhere the probability
of experiencing a valuelessthan that is 80%?
Solution:
As suggested before, it is important and helpful to sketch the distribution.