Download Normal Distributions

6.3 Continuous Random
Variables and the Normal
Probability Distribution
Objectives:
By the end of this section, I will be
able to…
1)
Identify a continuous probability
distribution.
2)
Explain the properties of the normal
probability distribution.
Collect and analyze all the GPAs of
your fellow classmates.

Its Continuous because you can
have a GPA anywhere between 0.0
and 4.5 (depending on your phasing)

Example of Continuous
Random Variable.
Finding Probabilities of
Continuous Distributions

It is represented by area under the curve.
As you increase your sample size,
your data will begin to resemble s
smooth curve.

This smooth curve eventually becomes
the NORMAL DISTRIBUTION.

How does this relate to
Normal Distributions?
Video: 4:50
Normal
Distributions
The mean is at the center
2.
Mean = median
3.
The scores tend to be ± 3 standard deviations
away from the mean.
Why does ±3 standard deviations sound so familiar?
(Think back a little bit!)
1.
Normal Distributions
{


What is the mean? 100
The standard deviation? 15
What is the mean? 6
 The standard deviation?

2
The Empirical Rule.
Used only when a distribution is bell-shaped.
Which is another word for a NORMAL
DISTRIBUTION.
The Empirical Rule.
Using the Empirical Rule
Assume the average GPA for the class is 3.20
(I am probably being a little too generous!)
with a standard deviation of 2 pts.
 Draw the Curve.
 Find the probability of having a GPA less
than 3.20.
 Find the probability of having a GPA more
than 3.60 but less than 3.80.
