NORMAL DISTRIBUTIONSUBHRAT SHARMACUHP13MBA85

Normal distribution• Each binomial distribution is defined by n, the

number of trials and p, the probability of success in any one trial.

• Each Poisson distribution is defined by its mean• In the same way, each Normal distribution is

identified by two defining characteristics or parameters: its mean and standard deviation.

• The Normal distribution has three distinguishing features: • It is unimodal, in other words there is a single peak. • It is symmetrical, one side is the mirror image of the

other. • It is asymptotic, that is, it tails off very gradually on each

side but the line representing the distribution never quite meets the horizontal axis

Properties•  It is symmetric around the point x = μ, which is at

the same time the mode, the median and the mean of the distribution.

• It is unimodal: its first derivative is positive for x < μ, negative for x > μ, and zero only at x = μ.

• It has two inflection points (where the second derivative of f is zero and changes sign), located one standard deviation away from the mean, namely at x = μ − σ and x = μ + σ.

• It is log-concave• It is infinitely differentiable, indeed super

smooth of order 2

EXAMPLE

Probability density function

Cumulative distribution function

FORMULA

Importance of Normal Distribution• When number of trials increase , probability

distribution tends to normal distribution .hence , majority of problems and studies can be analysed through normal distribution

• Used in statistical quality control for setting quality standards and to define control l