NORMAL DISTRIBUTION: NORMAL DISTRIBUTION Presented by Aparna H S1 MBA IMK Kollam
Types of Distribution : Types of Distribution Frequency Distribution Normal (Gaussian) Distribution Probability Distribution Poisson Distribution Binomial Distribution Sampling Distribution t distribution F distribution
HISTORY OF NORMAL DISTRIBUTION: HISTORY OF NORMAL DISTRIBUTION Johann Carl Friedrich Gauss (1777 – 1855) Gauss used the normal curve to analyze astronomical data in 1809. The normal curve is often called the Gaussian distribution. In Germany, the portrait of Gauss, the normal curve and its p.d.f . have been put on their 10 Deutschmark Note.
HISTORY OF NORMAL DISTRIBUTION: HISTORY OF NORMAL DISTRIBUTION Pierre Simon Laplace(1749 – 1827) Laplace used the normal curve in 1783 to describe the distribution of errors. In 1810, he proved the Central Limit Theorem .
HISTORY OF NORMAL DISTRIBUTION: HISTORY OF NORMAL DISTRIBUTION Abraham De Moivre(1667 – 1754) The normal curve was developed mathematically in 1733 by De Moivre as an approximation to the binomial distribution. His paper was not discovered until 1924 by Karl Pearson.
Normal (Gaussian) Distribution : Normal (Gaussian) Distribution Total area enclosed is 1 Upper tail Line of symmetry Lower tail - μ
What is Normal Distribution?: What is Normal Distribution? The normal distribution is a continuous distribution and plays a very important and pivotal role in statistical theory and practice. Normal distribution is also known as Gaussian Distribution The normal distribution is a bell shaped curve.
What is Normal Distribution?: What is Normal Distribution? The normal curve is symmetrical and is defined by its mean and its standard deviation. The normal curve is not just one curve but a family of curves. Just as the equation for a circle describes the family of circles
What is Normal Distribution?: What is Normal Distribution? The equation for the normal curve describes a family of such curve which may differ only with regard to the values of mean and standard deviation , but have the same characteristics in all a other respect.
Characteristics of Normal Distribution: Characteristics of Normal Distribution The shape of the normal curve is often illustrated as a bell-shaped curve. The central values such as mean median and mode are identical All normal curves are symmetrical about the mean.
Characteristics of Normal Distribution: Characteristics of Normal Distribution The sum of the positive deviation from the median is equal to the sum of the negative deviations. The standard deviation determines the width of the curve. The height of the normal curve is at its maximum at the mean value.
Characteristics of Normal Distribution: Characteristics of Normal Distribution The height of the curve declines as we go in either direction from the mean, but never touches the base, so that the tails of the curve on both sides of the mean extend indefinitely. The total area under the curve the same as any other probability distribution is 1.
SHOWING DIFFERENCES IN S.D: SHOWING DIFFERENCES IN S.D
EQUATION……..: EQUATION…….. The number of standard deviations Z for an observation which is the distance between the value X and the mean in terms of number of standard deviations in the normal distribution is defined by: Z = x- μ σ
Contd……..: Contd…….. Z= Number of standard deviations . X=Value of the observation. μ =The mean of the distribution. σ = The standard deviation of the distribution.
Applications to business administration : Applications to business administration The normal distribution has applications in many areas of business administrations. For e.g. Modern portfolio theory commonly assume that the return of a diversified asset portfolio follow a normal distribution. In operations management, process variation often are normally distributed In HR management employees perform sometimes is considered to be normally distributed
Questions????: Questions???? Find out the probability that the standard normal variate lies between 0 and 1.2? Z=O Z= 1.2
Questions????: Questions???? Find out the probability that the standard normal variate lies between -1.5 and 0? Z=1.5 Z=0
Questions????: Questions???? Find the area under the normal curve between z=-1.4 and Z=1.2??? Z=-1.4 Z=0 Z=1.2
Question???: Question??? A set of examination mark is approximately normally distributed with a mean of 70 and a SD of 5.Find out the probability that getting more than 75 marks???
Thank you……: Thank you……