1. Provide an original real-world example of some practical case where we can use the normal distribution to make informed decisions. For this discussion, I want you to use the Standard Normal Distribution Table described within the weekly lesson. Include the following components within your response to this part:

(a) Briefly discuss your real-world example.

Consider the following example: *The distribution of IQ scores of children within a local school district is considered to be normally distributed. Let the continuous random variables x denote a child’s IQ score. **If =110=110 and =5=5, find P(xb)P(xb) , P(xa)P(xa), and P(axb)P(axb) . *[This is just an example to describe how you should present your specific example. I expect you to choose a different real-world example.]

(b) Identify your mean () and standard deviation (). Your needs to be about four time larger than your .

(c) Select any number “a” below or above the but not too far from it. The magnitude of the difference ( a – ) must be less than 3. The magnitude of the difference ( b – ) must also be less than 3. Your value for “a” must also be less than your value for “b.” Provide a brief statement that demonstrates that these requirements have been met.

(d) Find *P(xb)P(xb)*. **Show all work and discuss how you used the table for the standard normal distribution within the eText to determine this result**. Note: Express your computed z-score to the nearest hundredths place (e.g., z = 1.96).

(e) Find *P(xa)P(xa)*. **Show all work and discuss how you used the table for the standard normal distribution within the eText to determine this result**. Note: Express your computed z-score to the nearest hundredths place (e.g., z = 1.96).

(f) Find *P(axb)P(axb)*. **Show all work and discuss how you used the table for the standard normal distribution within the eText to determine this result**.

(g) Interpret each of your results for (d), (e), and (f) within the context of your original example.

**For this part, I expect original examples where all of your work is shown. Providing me with the correct answer with no work shown will get no credit. I am requiring you to use the standard normal table to determine each result. Other methods will not be accepted. **

For your convenience, click on the following link to access table: The Normal Distribution Table (Links to an external site.)

You can also use the Areas of a Standard Normal Distribution table within the Appendix section of your textbook if you encounter any issues accessing the table attached to this question.

2. Reply to at least TWO other student posts in a mathematically substantive way to contribute to this week’s discussion.

**All responses must be original. If you provide the same response as one of your other classmates or copy/paste information from other sources, you will receive no credit for your post. **

**All work must be typed within the provided discussion board fields. Do not submit attached Word files containing your response to any component of this discussion. No credit can be given for any photographed handwritten work that is submitted to the discussions.**