Question

This week we study Normal Distribution.

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

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(x<a).
To find P(x>a) use formula: P(x>a) = 1 - P(x<a)

Answer 1