The Normal Distribution,MBA Statistics Notes

The normal DistributionIn many natural processes, random variation is consistent with a probability distribution special called the normal distribution, which is the most commonly observed probability distribution. Mathematicians of Moivre and Laplace used this distribution in the 1700s. The beginning of the 19th century German mathematician and physicist Karl Gauss used to analyze astronomical data, and it became consequently known as the gaussienne distribution among the scientific community.The form of the normal distribution looks like that of a Bell, which is sometimes refers as "curve Bell", an example of which follows:

Normal distributionThe curve above is for a set of data with a mean of zero. In general, the normal distribution curve is described by the following probability density function:
Characteristics of Bell curve
The curve of bells has the following characteristics:
• Balanced
Unimodal •
• Extends up to +/-infinity
• Area under the curve = 1
Fully described by two parameters
The normal distribution can be completely defined by two parameters:
• average
• standard deviation
If the mean and standard deviation are known, then a primarily knows as much as if we had access to all points in the data set.
The rule of thumb
The rule of thumb is a handy quick estimate of the spread of the data account required of the average and standard deviation of a set of data that follows the normal distribution.
The rule of thumb indicates that for a normal distribution:
• 68% of the data fall within 1 standard deviation of the mean
• 95% of the data fall within 2 SD types of average
• Almost all (99.7%) data reporting to 3 standard deviations of the mean
Note that these values are approximations. For example, based on the normal curve probability density function, 95% of the data will be 1.96 standard deviations of the mean; 2 standard deviations is a convenient approximation.
Normal distribution and the Central theorem limits
The normal distribution is widely observed. In addition, it can often be applied to situations in which the data are distributed very differently. This scope of applicability is possible because the theorem central limit, which States that, regardless of the distribution of the population, the distribution of means of random samples approach a normal distribution for a large sample.
Applications for the Business Administration
The normal distribution has applications in many areas of the administration of affairs. For example:
• Modern portfolio theory commonly assumed that the performance of a diversified portfolio of assets follow a normal distribution.
• Management of operations, often changes in process are normally distributed.
• In the management of human resources, employee sometimes performance is considered be normally distributed.
The normal distribution is often used to describe random variables, in particular those with symmetric, unimodal distributions. In many cases however, the normal distribution is only an approximation of the actual distribution. For example, the physical length of a component cannot be negative, but the normal distribution extends indefinitely in both positive and negative directions. However, errors that result may be negligible or within acceptable limits, that to resolve problems with sufficient precision assuming a normal distribution.

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