# Week 5 Discussion: The Normal Distribution

Greetings Class Members !!

For grading purposes, this particular discussion posting area runs from Sunday Jan 31 through Sunday Feb 7, inclusively.

We explore the so-called Normal Distributions this Week. This includes normal probability distributions, the standard normal distribution, the standard normal distribution Table, the concept of continuous distributions, sampling distributions, and the Central Limit Theorem.

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Please don’t forget to use an “**outside**” resource as part of the content and documentation for your first Post – the Post which is due on or before Wednesday of the Week – the Post where you make the most major contribution to the Weekly discussion posting area and attempt to address the discussion prompts / cues for the Week. It could possibly include a web site that you discovered on the internet at large, so long as the web site is relevant and substantial and does not violate the Chamberlain University policy for prohibited web sites, and so forth. It could possibly include references / resources that you discover through making use of the online Chamberlain University Library ( please click Resources along the left and then click Library to discover the link to the Chamberlain University online Library ) . 🙂

Check out the link below for some information about the so-called Standard Normal Distribution. After that page comes up also click on the normal distribution link from that page to see some more useful and relevant information for our Week 5 concerns and COs.

Link (Links to an external site.)Links to an external site.

This is one kind of an example of using an “outside” source / resource to add to what is revealed in our Weekly Lesson in Modules and in our Weekly text book reading.

Please don’t forget to look over the Graded Discussion Posting Rubric each Week to be certain that you are meeting all of the Frequency requirements as well as all of the Quality requirements for graded discussion posting each Week.

If you have any questions about anything, please do not hesitate to post in the Q & A Forum discussion posting area or to send me a direct e-mail message to CSmith10@chamberlain.edu

Thanks Friends and Good Luck ! Work hard and learn a lot !!

Many variables in medicine follow a normal distribution where there are approximately an equal number of values below the mean as above the mean. Describe two variables that would probably follow a normal distribution. Also note which of the two variables would be likely to have a larger standard deviation and why.

Greetings Friends !!

One of the big initial questions this Week 5 involves which variable do you think has a larger standard deviation and why.

So I thought it would be good to point out and emphasize some of the implications of having a larger or smaller standard deviation.

So I copied a couple graphics from page 235 from another statistics text book for another Chamberlain statistics course and posted them here.

In the first graphic, we see that the distribution with the A designation has the smaller standard deviation because most of the data values occur over a smaller “range” or “segment” so to speak. In that first graphic, the data values for the B distribution are more “spread out” or have larger “variation” or “dispersion.”

So take in the example and then in the second graphic do the Try It Yourself exercise and Post your answers in response to that graphic. Then double check each other and make sure you all agree on the correct answers to the Try It Yourself exercise. In the example and in the Try It Yourself, pay attention to the questions involving means as well as standard deviations.

Thanks Friends and I am fairly convinced from my career that pictures and graphics are essential for better understanding in an introductory Statistics course.

Be well and have a Super day !!

**Reference**:

Larson, R. & Farber, B. (2015). * Elementary statistics: Picturing the world *(6th ed.). Boston, MA: Pearson.

**Required Resources**

Read/review the following resources for this activity:

- OpenStax Textbook: Chapter 2, 6, and 7
- Lesson
- Weeks 3 and 5 Excel Spreadsheets

**Scenario/Summary**

This week’s lab highlights the use of probability and normal distribution.

Follow the directions below to gather data, calculate using Excel spreadsheets, and interpret the results.

**Deliverables**

The deliverable is a Word document with your answers to the questions posed below based on the data you find.

**Required Software**

- Microsoft Word
- Microsoft Excel

**Demonstrate**

**Steps to Complete Week 5 Lab**

Use the Weeks 3 and 5 spreadsheets **from the Weeks 3 and 5 Lessons **to help you answer the questions below.

Step 1: __Your instructor will provide you with 10 values to use for this lab.__

**Gather 10 MORE of your own to add to the 10 provided by your instructor. Do the following:**

Survey or measure 10 people to find their heights. Determine the mean and standard deviation for **the 20 values** by using the Week 3 Excel spreadsheet. Post a screen shot of the portion of the spreadsheet that helped you determine these values. How does your height compare to the mean (average) height of the **20 **values? Is your height taller, shorter, or the same as the mean of the sample?

- Data Example of 10 people with different heights
**(your spreadsheet will have**—__20 values__**10 from your instructor and 10 from your own data gathering).**Step 2: Give some background information on the group of people you used in your study. You might consider using the following questions to guide your answer.- How did you choose the participants for your study? What was the sampling method:
**systematic, convenience, cluster, stratified, simple random**? - What part of the country did your study take place in?
- What are the age ranges of your participants?
- How many of each gender did you have in your study?
- What are other interesting factors about your group?

Step 3: Use the Week 5 Excel spreadsheet for the following.

- (Use the
**Empirical Rule**tab from the spreadsheet). Determine the 68%, 95%, and 99.7% values of the Empirical Rule in terms of the**20 heights**in your height study. - What do these values tell you?
- Post a screen shot of your work from the Week 5 Excel spreadsheet.

Week 5 Spreadsheet Example

- How did you choose the participants for your study? What was the sampling method:
- (Use the normal probability tab from the spreadsheet). Based on your study results, what percent of the study participants are shorter than you? What percent are taller than you?
- Post a screen shot of your work from the Week 5 Excel spreadsheet.
**Example:**If my height is 73 inches, then 20.86% of the relevant population is shorter. The other 79.14%, of course, is taller.

Step 4: Be sure your name is on the Word document, save it, and then submit it under “Assignments” and “Week 5: Lab”.

**Grading**

This activity will be graded based on the Week 5 Lab Rubric.

Dear Professor and classmates,

Our lesson states that many health-related measurements that would look like a bell curve or normal distribution, with half the values below the mean and half above, include birth weight and glucose levels (Chamberlain University, 2021). I don’t work with those variables much, so I looked into factors that affect heart disease to see if I could find a normal distribution. According to the Central Limit Theorem, if we take enough samples from a population that doesn’t have a normal distribution, the means of those samples will resemble a normal curve (Chamberlain University, 2021). I noticed this when I looked at weight. The information below came from Table 3 of the CDC’s National Center for Health Statistics Anthropometric Reference Data for Children and Adults: United States, 2015-2018 (NCHS, 2021) which is collected by way of a survey:

This set of statistics started with age 20 and is grouped by decades. If it had started with teenagers, we would see another column at the left of the histogram, probably a little lighter in Kg, balancing out this curve. The interesting thing about this report, is when you look at Table 9, the height charts, for comparison there were 5510 answers for women. I guess more women surveyed were willing to state their height but did not want to confess to their weight.

Elaine

Chamberlain University. (2021). MATH225. Week 5: Normal distribution (Online lesson). Downers Grove, IL: Adtalem.

U.S. Department of Health and Human Services, National Center for Health Statistics. (2021). Anthropometric reference data for children and adults: United States, 2015-2018 (NCHS Publication Series 3 No. 46). https://www.cdc.gov/nchs/data/series/sr_03/sr03-046-508.pdf

Good Morning Professor and Classmates,

The two variables that I work with that would probably follow a normal distribution are Hemoglobin and temperature. According to The National Center for Biotechnology Information (2020), hemoglobin takes place in the transportation of oxygen from the lungs to several tissues of peripheral. The LVV-morphine-7 is affected by bradykinin activities hence leading to blood pressure decrease. Hemoglobin acts as an endogenous inhibitor of enkephalin-degrading enzymes. Some of the enkephalin-degrading enzymes include DPP. It also acts as a selective antagonist of the P2RX3 receptor, especially in pain signaling. All the above properties influence it as a regulator of inflammation as well as pain. A normal range for hemoglobin is 14-18 g/dl for males and 12-16 g/dl for females. If someone’s hemoglobin is low, they are anemic.

The next variable that I mentioned is temperature. The temperature is measured at regular intervals to determine the level of illness that a person may have. The normal body temperature is 98.6 degrees (F), which will calculate as 37.0 degrees (C). If the body reaches 37.3 (C), this could be considered a low-grade fever. The higher the temperature, the dangerous it could become for the patient. Generally, a fever could be associated with a bacterial or a viral infection. The mean body temperature is consistently normal if the person is not ill.

In a distribution, when the mean = median = mode, then the curve is an asymmetrical bell curve, also known as a normal curve. The line of symmetry divides the curve in half—50% of the data is to the left of the line of symmetry and 50% of the data is to the right of the line of symmetry. This type of distribution holds for many health and medical measures such as birth weight, glucose levels, length of hospital stays, and so on.

“The standard deviation determines the width of the data set.” (Chamberlin University, 2020). The variance of hemoglobin is relatively large because the average Hg depends on the different disease processes of the individual. The average could be high or low. The temperature has a relatively low variance because the average body temperature is close in range. The high and low also depend on the disease process but the temperature is easily corrected than hemoglobin so therefore the standard deviation of hemoglobin is larger than the standard deviation of temperatures.

References

Chamberlin University (2020). Week 5 Lesson: Normal Distribution. https://chamberlain.instructure.com/courses/69745/pages/week-5-lesson-normal-distribution?module_item_id=9228501

National Center for Biotechnology Information (2020). PubChem Protein Summary for NCBI Protein P68871, Hemoglobin subunit beta.https://pubchem.ncbi.nlm.nih.gov/protein/P68871