Probability & StatisticsNORMAL PROBABILITY DISTRIBUTION

The normal distribution is commonly encountered in practice, and is used throughout statistics, natural sciences, and social sciences as a simple model for complex phenomena.The normal distribution arises in the study of numerous basic physical phenomena. Certain quantities in physics are distributed normally, as was first demonstrated by James Clerk Maxwell. The velocities of the molecules in the ideal gas have normal distribution.In science and engineering, it is often reasonable to treat the error of an observation as the result of many small, independent, errors. This enables us to apply central limit theorem and treat the errors as normal.One application deals with the analysis of items which exhibit failure due to wear, such as mechanical devices. Frequently the wear out failure distribution is sufficiently close to normal that the use of this distribution for predicting or assessing reliability is valid.Another aspect of this application is in quality control procedures. The basis for the use of normal distribution in this application is the central limit theorem which states that the sum of a large number of identically distributed random variables, each with finite mean and variance, is normally distributed. Thus, the variations in value of electronic component parts, for example due to manufacturing, are considered normally distributed.The normal distribution has applications in many areas of business administration. For example: Modern portfolio theory commonly assumes that the returns of a diversified asset portfolio follow a normal distribution. In operations management, process variations often are normally distributed. In human recourse management, employee performance sometimes is considered to be normally distributed.The normal distribution often is used to describe random variables, especially those having symmetrical, unimodal distributions. In many cases however, the normal distribution is only a rough approximation of the actual distribution. For example, the physical length of a component cannot be negative, but the normal distribution extends indefinitely in both the positive and negative directions. Nonetheless, the resulting errors may be negligible or within acceptable limits, allowing one to solve problems with sufficient accuracy by assuming a normal distribution.

Muhammad Ahsan KhanCE-119SE Civil EngineeringSection B