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Normal versus abnormal distributions.

will look at normal versus abnormal distributions. In a normal distribution, there is symmetry about the mean. This means that data in the middle of the bell curve occurs more frequently than data further away from the mean. A normal distribution is one of the most important probabilities in statistics, as it fits many natural phenomena. See the image below for a normal distribution of dice rolling.
The rolling of dice is a good example of normal distribution. In an experiment, it has been found that when one die is rolled 100 times, chances to get ‘1’ are 16.7%. If we roll the die 1000 times, the chances to get ‘1’ are, again, the same—16.7%. If we roll two dice simultaneously, there are 36 possible combinations. However, the probability of rolling ‘1’ (with six possible combinations) again averages to around 16.7%, (6/36). The more dice you roll, the larger the normal distribution graph.
Let’s say that you want ‘1’ to come up more often than just 16.7%. So, you alter the sides on each die, changing numbers 2 and 3 to 1. This results in rolling ‘1’ more often than the normal distribution. This would be an abnormal distribution and would skew the results. A normal distribution is one in which the mean, median, and mode coincide with each other and make the curve we see in the dice image above. By altering the dice, the curve shifts as seen in the image below, and the mode, median, and mean no longer align.
As a leader at E-City’s university, you decide to run a regression analysis to see if workforce education level is associated with annual sales volume in the region. Then, you decide to run a regression analysis to see if workforce skills are related to annual sales volume. You find that one of these analyses produced abnormal results.
First, download the data that you will need for this week’s project
Regression Analysis Data for E-City.xlsx

Then answer the questions below.

  1. Out of the two regression analyses, which outcome is normal?
  2. What is the R2 number of the regression that you ran with workforce education level as the X variable and annual sales volume as the Y variable?
  3. Describe how you would use these regression results for further analyses. Describe what you think the outcomes mean.

Sample Solution

competencies for Lush include experienced management, influential brand values, and customer engagement. Lush’s original founder, Mark Constantine, is still extremely involved in the organization and its vision development (Sander, 2018). Furthermore, as stated previously, Mr. Constantine has started two companies in the same industry previously. As a result, he has developed a great deal of practical experience which is beneficial for the entire organization. The values that are portrayed by the Lush company are embraced by consumers quite strongly. Since lush is a leader in the movement for cosmetic companies to be environmentally friendly and protect animal rights, consumers often choose them over other brands (Saner, 2018). Consequently, the organization can use its role as an industry ethical leader as a competitive advantage. Furthermore, the competency is more than sustainable due to their adoption of new causes regularly. Some causes that have been recently adopted are unethical police practices, the transgender movement, and denouncing the wrongful imprisonment of individuals based on ethnic identity (Saner, 2018). Consumer engagement is by far one of the greatest competencies the Lush brand has. When entering a Lush store, one would quickly find friendly and helpful service, an intriguing space, and the ability to interact with the products in depth before making a purchase. Furthermore, the competency will become even greater after the initiatives the company has adopted are established. For example, the use of product demonstrations will only increase the consumer satisfaction and make product value expectations better match actual product value. It is also important to note that these product demonstrations allow associates to further interact with customers as they enter. As a result, the organization will experience a stronger stance in their competition with other organizations.

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