Question

Discuss the following in 175 words: How normal distributions play a significant role in managerial decision-making.

Answer 1

The normal distribution, which is also called a Gaussian distribution, bell curve, or normal curve, is commonly known for its bell shape (see Figure 1) and is defined by a mathematical formula. It is a member of families of distributions such as exponential, monotone likelihood ratio, Pearson, stable, and symmetric power. Many biological, physical, and psychological measurements, as well as measurement errors, are thought to approximate normal distributions. It is one of the most broadly used distributions to describe continuous variables.

Figure 1 The Normal Distribution

The normal curve has played an essential role in statistics. Consequently, research and theory have grown and evolved because of the properties of the normal curve.

Businesses need accurate data about the market in which they operate so that they can meet the needs of their customers. Analyzing the distribution of that data helps ensure that business decisions are not made based on a group that doesn't actually represent the larger group as a whole.

When researchers choose a group to study, the selected group is called a sample and the larger group that the sample should represent is called a population. For example, the college students and the NRA members in United States are both samples and everyone in the United States is the population.

Now, it's very important for businesses to make sure their data is normally distributed, in other words, verified to represent the population that is being studied.

Many things in business follow a normal distribution, but I think you’ll find most of those in e.g. manufacturing. If by business you meant finance, it still have good uses, such as to describe uncertainty about the estimated parameters of other probability distributions, because MLE results are normally distributed.

However, financial data itself (returns, trading volumes, etc) are most emphatically not normally distributed, and ignoring that results in models that instruct us to take on monstrous risk; they work well most of the time (tail events are rare, after all), but then they blow up (tail events are not that rare).

The normal distribution is important is that a wide variety of naturally occurring random variables such as heights and weights of all creatures are distributed evenly around a central value, average, or norm (hence, the name normal distribution). Although the distributions are only approximately normal, they are usually quite close.