Normal Approximation to the Binomial Distribution by susu

Normal Approximation to the Binomial Distribution by susu
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2015-03-03 02:59
This example demonstrates the comparison between the probability mass function of the binomial distribution and the probability density function of the normal distribution, illustrating how the normal distribution approximates the binomial distribution. Key mathematical concepts include binomial distribution, normal distribution, probability & statistics, and integral calculus from differential calculus. The construction uses GeoGebra commands/objects: BinomialDist (binomial distribution), Normal (normal distribution), Point (point), Integral (integral), and objects: n (number of trials), p (probability of success), a (lower limit of integral), f (function), b (upper limit of integral), A (point), xa (point), c (point), d (point), text1 (text), text2 (text), text3 (text). It is suitable for high school and above students to understand the central limit theorem in probability statistics and its application, or for teaching integral calculations in differential calculus.

GeoGebra Commands & Parameters

  1. BinomialDist(n, p) → a
  2. Normal((n * p), sqrt(((n * p) * (1 - p))), x) → f
  3. Point(xAxis) → A
  4. Integral(f, -100, xa) → c
  5. BinomialDist(n, p, xa, true) → d