http://www.ck12.org Chapter 15. Concepts of Statistics
15.6 The Normal Curve
Here you will define the standard normal distribution and learn how standard deviation and the area under the curve
are connected.
When students ask their teachers to curve exams, what they often mean is they want everyone to simply get a higher
grade. Curving a grade can also mean fitting to a bell curve where lots of people get Cs, some people get Ds and
Bs and very few people get As and Fs. Even though this second interpretation is not what most students mean, the
normal curve is one of the most widely used and applied probability distributions. What are other examples that
follow a normal distribution?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/62995http://www.youtube.com/watch?v=hgtMWR3TFnY Khan Academy: Introduction to the Normal Distribution
Guidance
TheStandard Normal Distributionis graphed from the following function and is represented by the Greek letter
phi,φ.
φ(x) =√^12 πe−^12 x^2
This distribution represents a population with a mean of 0 and a standard deviation of 1. The numbers along the
x-axis represent standard deviations. For data that is normally distributed, theempirical rulestates that:
- Approximately 68% of the data will be within 1 standard deviation of the mean.