Find an example of application of Normal Distribution (or approximately Normal Distribution) in your workplace or business (or any other business that you are familiar with). Prove that the variable has the characteristics of a Normal Distribution. Recall that the variable must be continuous and the distribution must be symmetrical (or approximately symmetrical). For a distribution to be approximately Normal, the values of Mean, Median, and Mode must be fairly close.
Very few things in the real world have continious variables, we count and measure things as integers (number failures, boxes leaving shipping, etc). However, if you look at the Poisson distsribution, which is for discrete variables (not continous), as the frequency per interval rises (lambda in the link), you see if you "connect" the dots, it very much approaches the Normal distribution. The math on the Normal distribution is much easier, as calculus can be used to find the area under the graph (cumulative probability). So in the Real world, even when we deal with real countable objects, we can use the Normal distribution even we do not have continous variables (if the incidence for each event is measured over a large number of events.
So much for philosophy: However, you can see from this arguement, the normal distribution can be used for number of boxes expected per hour, cars on a bridge per hour, and etc, even though these are not continous variables.
I would pick the following: Error rate on keyboard entries, or time to type 100 words by data transcribers, or just anything like that.
Good luck.
In my workplace, which is an e-commerce company, we often analyze the shipping time for our products as an example of the application of normal distribution. Let's go through the steps to prove that this variable has the characteristics of a normal distribution.
1. Continuous Variable: The shipping time can be measured in hours or days, providing a continuous scale.
2. Symmetry: To demonstrate symmetry, we can plot a histogram of the shipping time data and check its shape. When the data is symmetrical, the histogram will resemble a bell-shaped curve.
3. Mean, Median, and Mode: We need to ensure the mean, median, and mode are fairly close in order to show that it is approximately normally distributed. Let's assume we have collected data on the shipping time for a large number of orders.
- Mean: Calculate the average shipping time by summing up all the individual shipping times and dividing it by the total number of orders.
- Median: Arrange the shipping times in ascending order and find the middle value. If there is an even number of data points, take the average of the two middle values.
- Mode: Identify the value with the highest frequency of occurrence in the dataset.
If the mean, median, and mode are all close in value, it suggests that the data is approximately normally distributed.
4. Hypothesis Testing: We can further confirm the normal distribution using statistical tests like the Shapiro-Wilk test or Anderson-Darling test. These tests assess the data against the null hypothesis that it follows a normal distribution. If the p-value obtained from the test is greater than the significance level (usually 0.05), it indicates that the data does not significantly deviate from a normal distribution.
By conducting these steps in our e-commerce company, we can determine whether the shipping time variable satisfies the characteristics of a normal distribution or is approximately normally distributed.