University of Southern California Ch 6 Normal Distribution Paper Chapter 6:The Normal Distribution This week we study Normal Distribution. First, see all

University of Southern California Ch 6 Normal Distribution Paper Chapter 6:The Normal Distribution

This week we study Normal Distribution.

First, see all material posted in week 9.
Also read sections 6.1, 6.2, 6.3 in Chapter 6 of the eText.
Then, post your submission for Part 1 and Part 2 below.

Part 1. Demonstrate that you understand basic concept of Normal Distribution.
In two small paragraphs describe a couple of properties/rules of Normal distribution.

Hint: look for KEY FACTS and DEFINITIONS in sections 6.1 and 6.2 of eText.

Give one example of some practical case where we can use Normal distribution (for instance, IQ scores follow a normal distribution of probabilities with the mean IQ of 100 and a standard deviation around the mean of about 15 IQ points.)

Part 2. Assign your numbers for mean μ and standard deviation σ.
Make sure μ is about four times bigger than σ.

Then select any number “a” below or above mean μ,
but not too far from μ , difference (a – μ) should be less than 3σ.
For example, μ = 80, σ = 20, a = 90 (or a = 75).

Find following two probabilities:

1) P(x < a) 2) P(x > a)

First, use formula: z = (a – μ)/σ to calculate z-value
and then use Appendix Table for Standard Normal Distribution.
You can find tables in Appendix to our eText or attached below.

Remember, Appendix Table gives you probability P(xa) use formula: P(x>a) = 1 – P(x