Download Normal Distribution

Math 20-2
Statistics: Lesson #4
The Normal Distribution
Objective: By the end of the lesson, you should be able to:
- Explain the properties of a normal curve, including the mean, median, mode, standard
deviation, and area under the curve.
- Determine if a data set approximates a normal distribution.
Key Point: One of the most important and frequently occurring statistical distributions is the
normal distribution.
If the sample studied is large enough, many measurements in real life follow a normal
distribution (e.g. height, mass, intelligence, etc.) When graphed as a histogram or frequency
polygon, the normal distribution has a bell shape, and is often referred to as the Bell Curve.
Frequency
Normal Distribution Curve
(The Bell Curve)


Mark the mean, median, and mode on the normal curve above.
How much of the data is below the mean? How much is above the mean?
Properties of a Normal Distribution:

The mean, median, and mode are ______________.

The graph is symmetrical about the mean, i.e. _______ of the data is lower than the mean
and _______ is larger than the mean.

The total area under the curve represents ________% of the data.

Almost all the data lie within _____ standard deviations of the mean (________________
__________________________).
Math 20-2
Statistics: Lesson #4
The 68-95-99 Rule:

About _________% of the population is within 1 standard deviation of the mean.

About _________% of the population is within 2 standard deviations of the mean.

About _________% of the population is within 3 standard deviations of the mean.
  3
  2
 

 
  2
  3
e.g. 1) Look at the data collected for the whole class’ rolls of two dice. Does this data
approximate a normal distribution? Explain why or why not.
Math 20-2
Statistics: Lesson #4
e.g. 2) A company has determined that the lifetime of the car battery it produces is normally
distributed with a mean of 6 years and a standard deviation of 11 months.
a) Sketch a graph of this distribution. Label the divisions on the horizontal axis.
b) What percent of batteries will have a lifetime of 50 to 83 months?
c) Out of a shipment of 450 batteries, how many would you expect will have a lifetime
over 61 months?
d) If the company wants to offer a warranty on its batteries. For how many months
should the batteries be covered by the warranty if the manufacturer wants to replace
no more than 2.5% of the batteries sold?
Assignment:
p. 279-282 #1, 6-7, 9-11, 16