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Disccusion 1

When comparing data from different distributions, what is the benefit of transforming data from these distributions to conform to the standard distribution?

When comparing data from different distributions, transforming that data to conform to the standard distribution allows one to determine the data presented, compare, and evaluate. By making the distributions normal, one can quickly determine the percent of values that fall between a range, where a value falls relative to others. Also, standard distribution enables one to standardize all the data and answer any inquiries concerning the data sets being compared. For example, the standard distribution can give percentages of the probability of an occurrence above/below the mean for all data collections.Overall, transforming data benefits by presenting researchers the required material they need to calculate scores with different parameters (Tanner, 2016).

What role do z scores play in transforming data from multiple distributions to the standard normal distribution?

Transforming to a z-score allows one to use a single table (standard normal) to evaluate probabilities. According to Crash Course Statistics #18, expressed that "z-scores, in general, allow us to compare things that are not on the same scale, as long as they are normally distributed" (2018). Z scores are explicitly the formula most generally employed to transform scores and data from any standard normal distribution. Once transformed, the z score allows researchers to compare and contrast the variables they have encountered in the distribution that are not similar to another.In addition, it can improve interpretation, particularly when comparing across variables with very different scales and means.

What is the relationship between z scores and percentages?

From my understanding, if one knows z-score, they can use it to find the percentage of values in collecting numbers within a given region. In this case, an individual discussing a particular statistical requirement with an educator and determining if they want to know the percentage of numbers in the data set are either below/above the value associated with their z-score. Overall, by using the z-score, one can locate a percentage under the standard normal distribution. Moreover, the z-score allows for calculating an area percentage anywhere along a standard normal distribution curve (Tanner, 2016).

Give an example of a variable likely to be normally distributed in the population and explain how z scores pertaining to that variable would be useful in a real-life situation.

An example of a variable likely to be normally distributed in the population is how several males over the age of 60 are obese. The z scores would help calculate the probability of a male being obese when he approaches that age.Another example is if one has a collection of students' SAT scores with perfect normal distribution. One may require to know what percentage of students scored above 2,000, which one can calculate as having a corresponding z-score of 2.85.

Disscusiion 2 needs separate feedback

When comparing data from different distributions, the benefit of transforming data from these distributions to conform to the standard distribution is to compare data to other available data.

The role thatzscores play in transforming data from multiple distributions to the standard normal distribution is that it recalibrates to fit a distribution where the mean is 0, and the standard deviation is 1.0 (Tanner, 2016).

The relationship betweenzscores and percentages is that the percentage will always be in azscore table with its decimal value between 0 and 1.0.

An example that is likely to be normally distributed in the population would be someone's height. An example of how azscore would be useful in a real-life situation is the stock market.

Dissscusion 3 also needs feedback

When comparing data from different distributions the benefit of transforming it to conform to the standard deviation is because of the fixed values and this makes the data easier to understand. This allows a researcher to take data from a sample and make decisions about the entire population. We can be confident in answering questions about any normal data using the standard normal distribution (Tanner, 2016).

We get a z score by taking two things that are measured in different ways and making them comparable through an equation (CrashCourse, 2018).This equation is called z-transformation and is found by subtracting the mean of a data set from each score that you want to transform and dividing it by the standard deviation of the data set. By doing this, we are able to accurately compare two things that are measured differently to each other.The Crash Course video #18 used the example of ACT and SAT scores. Both tests are measured differently but by using z transformation we can compare an ACT to an SAT score and tell which was higher. The relationship of z score to percentage is that we can find the z score from a percentage by working the transformation equation backwards (Tanner, 2016).

In real life, knowing the z score would be helpful in a situation such as this: understanding the normal distribution of traffic patterns so that officers can be dispersed to areas of high congestion to help alleviate the congestion and accidents that occur because of it. By using data gathered from traffic cameras we will be able to predict the times and places in the city that major traffic congestion will occur, and assign officers to direct traffic and prevent accidents.