## reply the discussion question then reply two students

### reply the discussion question then reply two students

### Question Description

Can you help me understand this Business question?

question(250 words):

After explaining what a normal distribution is, name and explain three business processes that can be described by a normal distribution.

reply#1

The shape of the graphic normal distribution is an upside-down bell. The very middle line represents the mean. The standard deviation sits on the X-axis away from the mean. When the standard deviation gets closer to the mean, the curve gets steeper; likewise, when it gets far, the curve turns to flatten.

The normal distribution represents how the sample values deviate from their mean. Larger is the standard deviation, more different are the sample values from their mean. This conception could be widely applied to many business processes. For instance, it is used to measure the risk of a stock. When the standard deviation gets bigger, it means volatility and associated risk turns higher.

It could also be used in Six Sigma. When the processing engineer tries to measure how a machine or process performs. They can employ normal distribution as well. When the standard deviation turns to be smaller, their effort would most likely be paying off. HR is another field where the normal distribution is widely used. We could use it to dynamically demo how the salary expense is distributed within the organization, protecting fairness and team morale.

Reference:

“Lesson 4” (2020). California Institute of Advanced Management. https://ciam.instructure.com/courses/457/files/341176/download?wrap=1

#2

The normal distribution is a probability function that demonstrates how the values of a variable are distributed evenly around the mean (Frost, n.d.). It is symmetric because most of the observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions. Extreme values in both tails of the distribution are similarly unlikely. Data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distribution will appear as a bell curve (Chen, 2020). It has the following features:

- symmetric bell shape
- mean and median are equal; both located at the centre of the distribution
- $≈68%$
- $≈$95% of the data falls within two standard deviations of the mean
- $≈99.7%$

The normal distribution can be applied to many areas of business administration:

- Modern portfolio theory (MPT) often assumes that the return of a diversified asset portfolio is normally distributed. MPT offers a systematic mathematical approach which aims to maximize a portfolio’s expected return for a given amount of portfolio risk by selecting the proportions of various assets (Costa et al., 2015; Seth, 2019).
- The normal distribution curve is one of the most important statistical concepts in Six Sigma. In Six Sigma, variations are typically modelled with the bell-curve normal distribution, which visualizes the variation in a dataset. The central idea behind Six Sigma is measuring the number of “defects” in a process and figuring out how to eliminate them in order to get the process more in line with its goal (Roseke, 2020).
- The normal distribution can also be used for inventory forecasting. Applying normal distribution analysis to inventory produces forecasts and estimates based on previous performance of business clients and suppliers, refining the way a business predicts its future business activity.