- What are the basic differences between the two distributions? Binomial distributions tell the probability of success or failure in a given set of trials. An example that has been frequently used is that of a coin toss. There are only two possible outcomes when the con is flipped- heads or tails. Unlike normal distributions, there is a finite amount of events.

Normal distributions can be described by their mean and standard deviation. Normal distributions are based on values in a given data set. There are continuous data points and an infinite amount of events.

The major difference between normal distribution and binomial distribution is that normal distribution, describes continuous data with a symmetrical distribution specifically designed as a bell shape when on a table or graph. Whereas, binomial is distribution of binary data from samples where each observation can be summarized as â€œa success or failureâ€� (Gertsman, B. (2015).

- Under what circumstances do you think it works well to approximate the binomial using the normal, considering the differences?

If there are large n values, it would be simpler to use normal approximation.

When you employ a continuous distribution (the normal distribution) to approximate a discrete distribution, you get the normal approximation to the binomial (the binomial distribution). If the sample size is large enough, the sampling distribution of the sample means becomes approximately normal, according to the Central Limit Theorem.

The binomial distribution must have a shape that is comparable to that of the normal distribution. The values np and nq must both be greater than five (np>5 and nq>5) to achieve this; a better estimate is if they are both greater than or equal to ten.

- Under what public health or medical circumstances would it be helpful to identify the probability of an event? Provide some real-life examples.

One thing that came to mind with this question is drug trials. In a drug trial, there would be a specific number of participants being given a specified drug. The outcomes for treatment would be success or failure. If 8 out of 10 patients experience positive outcomes over a specified period of time, we could say that it is probable that 8 out of every 10 people would experience the same result.

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.

For example, in medicine, probability is increasingly widely employed in survey data analysis, such as when a 10% connection between people’s disease and their behavior statements is supposed to imply, for instance, that general behavior A has a 10% risk of producing illness B. Frequently, general behavior A has no effect on sickness B, but it does have some link with the usage of an unnamed product C, which is the true cause of illness B. However, the inaccurate medical claim is being promoted.