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)...

The manager notes a strong positive correlation between the two variables, indicating that the more employees on the floor, the higher the hourly sales. However, upon inspection of the graphical display, the retail store manager notes that the relationship is actually curvilinear in nature. Specifically, the hourly sales increase with more sales employees on the floor up to a point (five employees), after which the hourly sales plateau and even begin to decline slightly. The manager deduces that having more than five employees on the floor at any time may interfere with the customers' typical shopping practices, thus distracting them from making purchases.
In conclusion, probability distributions and the normal distribution are not directly used in business decision-making. However, these concepts form the basis of most statistical tests, depending on the underlying assumptions of the particular test. These tests aid a business manager to make inferences of a particular concept from a smaller sample to predict outcomes in the population as a whole.

References

Berenson, M.L., Levine, D.M., & Krehbiel, T.C. (2001). Basic Business Statistics: Concepts and Applications. Upper Saddle River, NJ: Prentice Hall.

Cleophas, T.J. (2004). Clinical trials: Renewed attention to the interpretation of the P. values -- review. Am J. Ther, 11(4), 317-322.

Healy, M.J. (1994). Statistics from the inside. 13. Probability and decisions. Arch Dis Child, 71(1), 90-94.

Ludbrook, J. (1995). Issues in biomedical statistics: comparing means under normal distribution theory. Aust NZJ Surg, 65(4), 267-272.

Wessels, W.J. (1993). Economics: Barron's Educational Series.