quants
Using the Normal Distribution
The normal distribution is a very commonly occurring continuous probability distribution—a function that tells the probability that any real observation will fall between any two real limits or real numbers, as the curve approaches zero on either side. Normal distributions are extremely important in statistics and are often used in the natural and social sciences for real-valued random variables whose distributions are not known (Casella and Berger, 2002). This essay will discuss the use of Normal Distribution in a business and in real life.
Statistics is used a lot everyday in life, in many cases without the person doing so even realizing it. An example of that can be that for instance a new teacher enters a classroom and notices that all the students are shorter than 5 feet. The teacher probably must have expected most students to be around the average height, maybe spotting just one or two students under 5 feet. In this judgment the teacher is actually employing the Normal Distribution. There are numerous things that display the same characteristic including body temperature, shoe size, IQ score and diameter of trees are a few of them.
The normal distribution has applications in many areas of business administration. For instance:
Modern portfolio theory commonly assumes that the returns of a diversified asset portfolio follow a normal distribution.
In operations management, process variations often are normally distributed.
In human resource management, employee performance sometimes is considered to be normally distributed.
The normal distribution often is used to describe random variables, especially those having symmetrical, unimodal distributions. In many cases however, the normal distribution is only a rough approximation of the actual distribution. For example, the physical length of a component cannot be negative, but the normal distribution extends indefinitely in both the positive and negative directions.
The normal distribution is a very commonly occurring continuous probability distribution—a function that tells the probability that any real observation will fall between any two real limits or real numbers, as the curve approaches zero on either side. Normal distributions are extremely important in statistics and are often used in the natural and social sciences for real-valued random variables whose distributions are not known (Casella and Berger, 2002). This essay will discuss the use of Normal Distribution in a business and in real life.
Statistics is used a lot everyday in life, in many cases without the person doing so even realizing it. An example of that can be that for instance a new teacher enters a classroom and notices that all the students are shorter than 5 feet. The teacher probably must have expected most students to be around the average height, maybe spotting just one or two students under 5 feet. In this judgment the teacher is actually employing the Normal Distribution. There are numerous things that display the same characteristic including body temperature, shoe size, IQ score and diameter of trees are a few of them.
The normal distribution has applications in many areas of business administration. For instance:
Modern portfolio theory commonly assumes that the returns of a diversified asset portfolio follow a normal distribution.
In operations management, process variations often are normally distributed.
In human resource management, employee performance sometimes is considered to be normally distributed.
The normal distribution often is used to describe random variables, especially those having symmetrical, unimodal distributions. In many cases however, the normal distribution is only a rough approximation of the actual distribution. For example, the physical length of a component cannot be negative, but the normal distribution extends indefinitely in both the positive and negative directions.
References: Casella, G. and Berger, R. (2002). Statistical inference. 1st ed. Australia: Thomson Learning. Isixsigma.com, (2014). Dealing with Non-normal Data: Strategies and Tools. [online] Available at: http://www.isixsigma.com/tools-templates/normality/dealing-non-normal-data-strategies-and-tools/ [Accessed 6 Jul. 2014]. Ross, S. (2005). Introductory Statistics. 1st ed. Burlington: Elsevier Science. Statweb.stanford.edu, (2014). No Title. [online] Available at: http://statweb.stanford.edu/~naras/jsm/NormalDensity/NormalDensity.html [Accessed 5 Jul. 2014]. Appendix Figure1 (www.isixsigma.com)