• 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
• 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
• It is symmetric around the point x = μ, which is at the
same time the mode, the median and the mean of the
• 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
Probability density function
• 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