Question

This week we study Normal Distribution. First, see all material posted on Blackboard in section: Course Material - 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. Part 2. Assign your numbers for mean ? and standard deviation ?. Make sure that ? is about four times bigger than ?. Select any number x below or above mean ?. Distance between x and ? should be less than 3?. Apply formula: z = (x - ?)/? and calculate z-value. Let's call the calculated z as zc. Then, use Appendix Table for Standard Normal Distribution (attached) and find probabilities: P(z < zc) which will be P(x < a) and P(z > zc) which will be P(x > a)

Answer 1

One example of some practical case where we can use Normal distribution.

Suppose we want to model the height of the people of the country, there we can use normal distribution to model.

Suppose we want to model the weight of the people of the country, there we can use normal distribution to model.

let ?=12 (? is taken 4 times bigger than ?) and ?=3.

let x = 11 (Here x is selected below the mean);

Here zc = 0.33

P(z<0.33) = 0.6293 ( From Table for Standard Normal Distribution )

P(z>0.33) = 0.3717 ( From Table for Standard Normal Distribution )

let x = 15 (Here x is selected above the mean);

Here zc = 1

P(z<1) = 0.8413 ( From Table for Standard Normal Distribution )

P(z>0.33) = 0.1587 ( From Table for Standard Normal Distribution )