Posted: February 26th, 2023

When responding to your peers, provide clarification where you can and/or ask questions to identify what in their response needs clarification, or provide an additional example of when each distribution could be used that relates to your peer's example.

Having reviewed the resources included in this module, draft one or two brief paragraphs addressing the following questions. Your responses must reference your course resources, and you are required to implement In-Text Citations and include a Works Cited page.

How did Frank Miller's approach to Batman change the public perception of the character?

What is one significant change that Miller brings to the character?

Does Miller's Batman have any similarities with the more light hearted version? (other than the obvious things like costume & gadgets)

Claudia Discussion:

1. Normal distributions apply to continuous random variables (Gerstman, 2014). Normal distributions have two parameters which are the mean (μ) and the standard deviation (σ). Normal distributions have an infinite range. Normal distributions utilize probability density functions to describe their continuous random variables (Gerstman, 2014). Binomial distributions apply to discrete random variables (Gerstman, 2014). Binomial random variables have two parameters which are the number of observations (n) and the probability of success for each observation (p). Binomial distribution use mass functions to describe their discrete random variables. Binomial distribution observations can only be categorized as successes and failures (Gerstman, 2014).

2. According to Gerstman (2014), when the number of observations (n) is large, binomial random variables can take on the characteristics of normal random variables. Normal approximation to the binomial can be used as a guide when npq is greater than 5.

3. It may be helpful to identify the probability of developing cancer, particularly in patients with a family history of a certain type of cancer or other risk factors. This information can be useful in the prevention, treatment, and control of cancer. Determining the probability of acquiring specific types of cancers at specific ages can be helpful for researchers and professionals in developing effective treatment plans and intervention strategies (The Institute for Work and Health, 2020).

**References:**

Gerstman, B. B. (2014). Basic Biostatistics (2nd ed.). Jones & Bartlett

Learning.

https://bookshelf.vitalsource.com/books/9781284066210

The Institute for Work and Health. (2010, October). Probability. Institute for Work and Health. Retrieved

February 14, 2023, from

https://www.iwh.on.ca/what-researchers-mean-

by/probability#:~:text=In%20epidemiology%2C%20probability%20theory%20is,the%20risk%20of%20health%20effects.Jolene Discussion:

1.
**What are the differences between binomial and normal distributions?**

Binomial and normal distributions can look rather similar under the right circumstances, but the greatest difference between the two is that binomial distributions are discrete, meaning that they have set data points with none in between, while normal distributions are continuous (Gerstman, 2015). An example of where a binomial distribution method could be used to analyze data would be a survey with yes and no as possible answers without the option of a ‘maybe’ such as do you brush your teeth twice a day, yes or no? An example where a normal distribution would be utilized would be analyzing data collected on the different birthweights of infants born at a particular hospital, where the possible number of potential birthweights are infinite.

2.
**Under what circumstances are normal distributions used to approximate binomial distributions?**

When X ≈ B (n, p), these normal distributions could be used to approximate a binomial distribution, especially if the number of observations is large or if np ≥ 5 (Gerstman, 2015). Large sample sizes could make it harder to determine the probability of a particular outcome, making it appropriate to approximate a normal distribution into a binomial distribution.

3.
**Under what public health or medical circumstances would it be helpful to identify the probability of an event?**

An example of a circumstance where public health could use probability is the calculation of the risk of having an adverse health event within a given period of time. A study looking at how COVID-19 affected mental health status in the United States used probability to predict how pre-pandemic factors such as prior mental health and physical health status as well as media consumption could predict pandemic-related stress and depressive symptoms (Holman, Thompson, Garfin, & Silver, 2020). The researchers used this data to predict who would be most likely to have negative mental health effects and determine where mental health services would be most beneficial, such as providing mental health resources to first responders and families who have directly been impacted by the virus.

References:

Holman, E. A., Thompson, R. R., Garfin, D. R., Silver, R. C. (2020). The unfolding COVID-19 pandemic: A probability-based, nationally representative study of mental health in the United States. Science Advances, 6(42). DOI: 10.1126/sciadv.abd5390

Gertsman, B. B. (2015). Basic Biostatistics: Statistics for Public Health Practice, 2nd Edition. Jones & Bartlett Learning.

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