The properties of a normal distribution include. It is symmetric and bell-shaped and the curve formed by a normal distribution is asymptotic to the x axis. Its median, mode and mean are positioned at the x axis’s midpoint, and both are equal. 50% of its values lie above the midpoint of the distribution whereas the other 50% lies below it.  68% of its area lies within one standard deviation of the mean, and 95% within two standard deviations of the mean, and the entire area beneath the normal curve is equal to 1.

The major reasons for the existence of an infinite number of normal distributions include the fact that the distribution arises in many statistics areas, and its mean is usually assumed to be normal. Thus, even if the population distribution from which the sample is obtained is not a normal one, the sample mean will be. Since a normal distribution is a continuous distribution and defined by the variance and the mean parameters, there are an infinite numbers of normal distributions. Also, since the variance of the distribution can take any non negative value or its mean be any actual value, then there are numerous values for them.

The main reason why one would assume that sample data represents a population distribution is mainly in endeavoring to make an inference about a population’s characteristics based on a sample of the population.

Normal distributions can be used in business decision making. For instance, decision makers can calculate the variances and means of particular projects to be undertaken and basing their decisions on these figures make a decision. They can also approximate the probabilities of success of these projects before deciding to undertake a given project. They can use probabilities to solve a particular problem they consider may affect the smooth running of the business. The use of variance also enables the decision makers to know the degree of risk associated with projects under consideration. This improves decision making in the firms involved.

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