Colorado State University Bell Curve Normal Distribution Discussion

I’m trying to learn for my Statistics class and I’m stuck. Can you help?

When one thinks of the normal distribution, the first thing that comesto mind is the bell curve and grades. While this is one example of anormal curve that is widely recognized, it is not the only one.

Read Example 1 and Example 2. Prepare a document explaining what you understand from the example 1 and example 2 separately. Add more information if possible to the examples. Your document should be minimum 250 words. Please have credible resources.

EXAMPLE# 1

SAT SCORES

The SAT test, taken before most students go to college, is a classicexample of a normal bell curve. Below please found the curve of SATscores from 2019, along with a chart listing the mean as well asstandard deviation (Staffroni, 2019).

As you can see, SAT scores form a classic bell curve. 68% of thedata falls within 1 standard deviation of the mean, 95% of the datafalls within 2 standard deviations of the mean, and 99.7% of the datafalls within 3 standard deviations of the mean (Khan Academy, 2020). Inthis case, the µ SAT score is 1059, and ?=210. So the interval µ-? toµ+? would equal 1 standard deviation, or 68% of the data. Thus 68% ofstudents have scores between 849 and 1269. µ-2? to µ+2? covers 95% ofthe SAT scores, thus 95% of students score between 639 and 1479. µ-3?to µ+3? covers 99.7% of the SAT scores, thus almost all students scorebetween 429 and 1600 (the maximum score).

References

Khan Academy. (2020). Normal distributions review. The Khan Academy. Retrievedfrom

https://www.khanacademy.org/math/statistics-probab…

Staffaroni, L. (Sep 29, 2019). SAT standard deviation: What does it mean for you? PrepScholar. Retrieved from https://blog.prepscholar.com/sat-standard-deviatio…

EXAMPLE# 2

? and ? determine the center and spread of the distribution. Theempirical rule holds for all normal distributions: 68% of the area underthe curve lies between (???, ?+ ?) 95% of the area under the curve liesbetween (??2?, ?+ 2?) 99.7% of the area under the curve lies between(??3?, ?+ 3?). The empirical rule states that for a normal distribution (Links to an external site.), nearly all of the data will fall within three standard deviations (Links to an external site.) of the mean (Links to an external site.).The empirical rule can be broken down into three parts: 68% of datafalls within the first standard deviation from the mean, 95% fall withintwo standard deviations, and 99.7% fall within three standarddeviations. (Stephanie, 2020)

Based on the data retrieved from GeoGebra (Normal Distribution: Chest Measurements, n.d.)

Mean chest size Std Dev

Men’s chest size 39.83 inches 2.05 inches

The ? is 39.83 and the ? is 2.05

??? to ?+ ? equals 1 standard deviation between 37.78 – 41.88 inches.

??2? to ?+ 2? equals 2 standard deviations between 35.73 – 43.93 inches.

??3? to ?+ 3? equals 3 standard deviations between 33.68 – 45.98 inches.

Based on the normal distribution we can assume that 99.7% of men have chest sizes between 33.68 and 45.98 inches.

Normal distribution: chest measurements. (n.d.). GeoGebra. Retrieved July 8, 2020, from https://www.geogebra.org/m/h3gwEk93 (Links to an external site.)

Stephanie, B. (2020, January 30). Empirical Rule ( 68-95-99.7): Simple Definition. Statistics How To. https://www.statisticshowto.com/empirical-rule-2