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The normal distribution law describes a distribution of data which are arranged symmetrically around a mean. The majority of data is close to this average, others are moving away gradually. This forms a normal distribution bell curve also called Gaussian curve.

Many physical quantities approach this normal distribution often described as the law of natural phenomena.

Even though there are many laws of probability, a phenomenon born of chance, reiterated many times, follows a probability that tends towards the normal distribution. This theorem is illustrated with the binomial distribution.

**Modify **parameters with the help of the sliders. **Click **and **drag **the a and b limits.

- Know the normal distribution and the influences of its parameters (average and variance)
- Know the binomial distribution and the influence of its parameters (number of trials, n, and the Bernoulli parameter, p).
- Show that the binomial distribution behaves like the normal distribution when the number of trials, n, increases (the Moivre-Laplace theorem).

A random variable Z follows a **normal distribution** N (μ,σ^{2}) if it provides a probability density p (x) which satisfies:

p(*x*) = 1/(σ√(2π)).exp( -(*x*-μ)^{2}/(2σ^{2}) )

where μ is the **mean**, σ…