Probability and Normal Distributions in

¶ … Probability and Normal Distributions in Business Decision-Making Statistical skills enable business managers to collect, analyze, and interpret data. These skills may provide a business leader with significant competitive advantage since business decisions are often based on inferences from data. Statistics may help in developing a model for refining business decisions, since these conclusions are often made with incomplete information. Statistical testing effectively uses the data that is available to improve business decision-making. Statistical techniques can test how large a part chance plays in the results reflected by the selected sample.

A manager must often estimate the characteristics of a population based on information provided by a sample chosen to yield an estimate of population characteristics. Confidence intervals are a mathematical statement of the level of confidence around the estimate. Today's global businesses face dynamic and complex markets. The environments in which these enterprises compete are constantly changing. Successful firms can develop strategies that enable them to be flexible in the changing world. These are firms that manage changes instead of reacting to changes.

In order for firms to become proactive in change management, they must be able to quickly analyze different strategies and the impact of different scenarios on the firm's performance. For companies in high technology industries, the dynamic and highly uncertain nature of their businesses makes rapid decision making a key for survival. Thus, it is crucial that businesses develop the capability to analyze business decisions and environments quickly without relying on costly, time-consuming studies and research.

Businesses should incorporate quality into products and processes and facilitate a process of continual improvement at all stages of manufacturing. The use of statistical methods results in processes that provide higher yields and product reliability than in the absence of such techniques. Carefully planned statistical studies minimize hindrances to quality and productivity at every stage of production, thus potentially saving time and money.

Although dozens of statistical tests may be applied across many business situations, the premise for many of these tests relates to two concepts: probability and the normal distribution. Probability is fundamental to the concept of statistical inference. Probability is an instrument used to measure the likelihood of the occurrence of an event, and utilizes the binomial distribution (Wessels, 1993). The concept of probability distributions plays an important role in analyzing business situations and in refining intuition.

Probability may be used to anticipate what the distribution of data may look like under a given model. Uncertainty allows one to generalize from a known sample with dichotomous outcomes to the unknown population and place a high degree of confidence in these findings. The normal distribution is a continuous symmetric distribution that follows a bell-shaped curve. Many measurement variables have distributions that are close to normal. Many frequently used statistical tests state the condition that the data are normally distributed.

The normal distribution is also important because the most robust statistical tests are derived from this distribution (Ludbrook, 1995). The normal distribution is paramount to the field of statistics. The normal distribution describes the manner by which continuous outcome estimators of population characteristics vary from sample to sample and, thus, serves as the foundation upon which statistical inference from a random sample to a population are made under these conditions.

Common statistical tests that are derived from the probability distribution include the chi-square, McNemar's test, and logistic regression (Berenson, Levine, & Krehbiel, 2001). An example of a business situation where the probability distribution may be utilized is a scenario where a manager attempts to predict employee retention. The statistical test would be a binary logistic regression analysis. The probability distribution is paramount to this example because it utilizes the dichotomous dependent variable of Yes/No (employee stays/employee quits).

Independent variables that may be used to predict employee retention include education level, length of employment, age, income, and gender. The output from this statistical test may help a business manager screen individuals before employment to assess whether the individual may stay or leave for another position. The majority of statistical tests use the normal distribution as a foundation. An example of a business situation that employs the attributes of the normal distribution is a supervisor who wants to assess spending habits between males and females in a retail store.

The outcome of interest, or the dependent variable, is average sales dollars per month, which is a continuous variable. Since the supervisor is interested in gender differences, gender (male/female) is entered as the independent variable in a two-sample t-test. The output of this test will determine the difference in monthly sales by gender as well as a confidence interval around this difference. If the confidence interval of the difference between genders does not include zero (Cleophas, 2004), one may assume that there is a difference between genders regarding spending habits.

Another example of the normal distribution contributing to decision-making involves a retail store manager trying to determine the optimal number of sales employees to have on the floor at any given time. The manager uses hourly sales as a benchmark to make this determination. A Pearson correlation test is constructed with number of sales employees on the floor as the independent variable (on the x-axis on a graphical display) and hourly sales as the dependent variable (on the y-axis on a graphical display).

The manager notes a strong positive correlation between the two variables, indicating that the more.