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Normal distribution

it is a ppt with just properties of normal curves. n few of other things about normal distribution.

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Normal distribution

  2. 2. • 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
  3. 3. • 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
  4. 4. Probability density function Cumulative distribution function
  5. 5. • 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