2. 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.

3.  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.

4.  It is represented by area under the curve. Finding Probabilities of Continuous Distributions

5.  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?

6. Video: 4:50 Video: 4:50

7. Normal Distributions 1. 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!)

8. { Normal Distributions

9.  What is the mean?  The standard deviation? 100 15

10.  What is the mean?  The standard deviation? 6 2

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

12. The Empirical Rule.

13.  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