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Normal Curve of Binomial Distribution

Normal Curve of Binomial Distribution
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2019-12-10 00:43
FunctionProbability & StatisticsGraphing
This example demonstrates how the binomial distribution approximates a normal curve with a large number of trials. Key mathematical concepts include binomial distribution and probability statistics. Using commands like If, Sequence, Max, Min, Polygon, Element, and Text, the binomial distribution's probability histogram is constructed and observed to approach a normal curve as the number of trials increases. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. If(i, 0, 1) → n
  2. Sequence(nCr[a, i], i, 0, a, 1) → l1
  3. Max(l1) → b
  4. Sequence(Element[l1, i] / 2^(a), i, 1, a + 1, 1) → l2
  5. Max(l2) → h
  6. Min(l1) → c
  7. Sequence((i, 0), i, 0, a) → l3
  8. Sequence((i - 1, Element[l1, i]), i, 1, a + 1) → l4
  9. Sequence(Polygon[Element[l3, i] - (0.5, 0), Element[l3, i] + (0.5, 0), Element[l4, i] + (0.5, 0), Element[l4, i] - (0.5, 0)], i, 1, a + 1) → l5
  10. Max(l2) → e
  11. Sequence((i / o - a / 2 / o, 0), i, 0, a) → l6
  12. Sequence(Polygon[Element[l6, i] - (1 / ((2 * o)), 0), Element[l6, i] + (1 / ((2 * o)), 0), Element[l6, i] + (1 / ((2 * o)), 0) + (0, Element[l2, i]), Element[l6, i] - (1 / ((2 * o)), 0) + (0, Element[l2, i])], i, 1, a + 1) → l7
  13. Sequence(nCr[a, i], i, 0, a, 1) → l1_1
  14. Max(l1_1) → b_1
  15. Min(l1_1) → c_1
  16. Polygon(Element[l3, r_2] - (0.5, 0), Element[l3, r_2] + (0.5, 0), Element[l4, r_2] + (0.5, 0), Element[l4, r_2] - (0.5, 0)) → q1, l, p, q, r_1
  17. Polygon(Element[l6, r_2] - (1 / ((2 * o)), 0), Element[l6, r_2] + (1 / ((2 * o)), 0), Element[l6, r_2] + (1 / ((2 * o)), 0) + (0, Element[l2, r_2]), Element[l6, r_2] - (1 / ((2 * o)), 0) + (0, Element[l2, r_2])) → q2, s, t, f_1, g_1
  18. Element(l1, r_2) → u
  19. Element(l2, r_2) → w
  20. Text("C(" + a + "," + r + ") = height =" + q1, A, true, true) → text2
  21. Sequence(nCr[a, i], i, 0, a, 1) → l1_2
  22. Max(l1_2) → b_2
  23. Sequence(Element[l1_2, i] / 2^(a), i, 1, a + 1, 1) → l2_1
  24. Max(l2_1) → h_1
  25. Min(l1_2) → c_2
  26. Max(l2_1) → e_1
  27. Element(l1_2, r_3) → u_1
  28. Element(l2_1, r_3) → w_1