6.3 Continuous Random Variables and the NormalProbability Distribution

Objectives:By the end of this section, I will beable 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.

It is represented by area under the curve.

Finding Probabilities of Continuous Distributions

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

1. The mean is at the center 2. Mean = median3. 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!)

{

Normal Distributions

What is the mean? The standard deviation?

100

15

What is the mean?

The standard deviation?

6

2

The Empirical Rule.

Used only when a distribution is bell-shaped.Which is another word for a NORMAL DISTRIBUTION.

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.

Using the Empirical Rule