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Normal distribution - Binomial distribution

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Summary

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.

Eventhough there are many lawsofprobability, aphenomenonbornof chance, reiteratedmanytimes, followsa probabilitythat tends towardsthe normal distribution. This theoremis illustratedwiththe binomial distribution.

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

Learning goals

  • 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).

Keywords

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A random variable Z follows a normal distribution N (μ,σ2) if it provides a probability density p (x) which satisfies:

p(x) = 1/(σ√(2π)).exp( -(x-μ)2/(2σ2) )

where μ is the mean, σ the standard…

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