5.1. Estimating the Mean and Standard Deviation of a Normal Distribution http://www.ck12.org
5.1 Estimating the Mean and Standard Devia-
tion of a Normal Distribution
Learning Objectives
- Understand the meaning of normal distribution and bell-shape.
- Estimate the mean and the standard deviation of a normal distribution.
Introduction
The diameter of a circle is the length of the line through the center and touching two points on the circumference of
the circle.
If you had a ruler, you could easily measure the length of this line. However, if your teacher gave you a golf ball
and asked you to use a ruler to measure its diameter, you would have to create your own method of measuring its
diameter.
Using your ruler and the method that you have created, make two measurements of the diameter of the golf ball
(to the nearest tenth of an inch). Your teacher will prepare a chart for the class to create a dot plot of all the
measurements. Can you describe the shape of the plot? Do the dots seem to be clustered around one spot (value)
on the chart? Do some dots seem to be far away from the clustered dots? After you have answered these questions,
pick two numbers from the chart to complete this statement:
“The typical measurement of the diameter is approximately __inches, give or take __inches.” We will
complete this statement later in the lesson.
Normal Distribution
The shape below should be similar to the shape that has been created with the dot plot.