MathPlotAI Logo MathPlotAI

Binomial Probability Distribution Interactive Demo

Binomial Probability Distribution Interactive Demo
Loading the math board and drawing, please wait…
2020-10-17 03:13
FunctionSequenceProbability & StatisticsSlider AnimationGraphing
① This GeoGebra example dynamically illustrates the binomial probability mass function alongside a normal approximation curve, allowing users to compare discrete and continuous distributions. ② Core mathematical concepts include binomial distribution, expected value, standard deviation, probability, and normal approximation. ③ Construction highlights: uses Textfield and InputBox for parameter inputs (n, p), BinomialDist command to generate binomial probabilities, Normal for the normal curve, Segment and Midpoint to build bar charts, and Sequence for generating data series. ④ Suitable for high school and college statistics courses, helping students visualize how the binomial distribution changes with parameters and understand the central limit theorem and probability calculations.

GeoGebra Commands & Parameters

  1. Textfield(n) → InputBox1
  2. Textfield(p) → InputBox2
  3. Textfield(l) → InputBox3
  4. Textfield(u) → InputBox4
  5. BinomialDist(n, p) → a
  6. Normal(m, s, x, false) → f
  7. Segment(B, A) → g
  8. Midpoint(B, A) → C
  9. Sequence(Polygon[(k - 0.5, 0), (k + 0.5, 0), (k + 0.5, BinomialDist[n, p, k, false]), (k - 0.5, BinomialDist[n, p, k, false])], k, l, u, 1) → l1
  10. Sequence(Polygon[(k - 0.5, 0), (k + 0.5, 0), (k + 0.5, BinomialDist[n, p, k, false]), (k - 0.5, BinomialDist[n, p, k, false])], k, u + 1, n, 1) → l2
  11. Sequence(Polygon[(k - 0.5, 0), (k + 0.5, 0), (k + 0.5, BinomialDist[n, p, k, false]), (k - 0.5, BinomialDist[n, p, k, false])], k, 0, l - 1, 1) → l3
  12. BinomialDist(n, p, l - 1, true) → r
  13. Normal(m, s, l, true) → w
  14. Normal(m, s, l - 0.5, true) → b_1
  15. BinomialDist(n, p, A14, false) → B14
  16. BinomialDist(n, p, A15, false) → B15
  17. BinomialDist(n, p, A16, false) → B16
  18. BinomialDist(n, p, A17, false) → B17
  19. BinomialDist(n, p, A18, false) → B18
  20. BinomialDist(n, p, A19, false) → B19
  21. BinomialDist(n, p, A20, false) → B20
  22. BinomialDist(n, p, A21, false) → B21
  23. BinomialDist(n, p, A22, false) → B22
  24. BinomialDist(n, p, A23, false) → B23
  25. BinomialDist(n, p, A24, false) → B24
  26. BinomialDist(n, p, A25, false) → B25
  27. BinomialDist(n, p, A26, false) → B26
  28. BinomialDist(n, p, A27, false) → B27
  29. BinomialDist(n, p, A28, false) → B28
  30. BinomialDist(n, p, A29, false) → B29
  31. BinomialDist(n, p, A30, false) → B30
  32. BinomialDist(n, p, A31, false) → B31
  33. BinomialDist(n, p, A32, false) → B32
  34. BinomialDist(n, p, A33, false) → B33
  35. BinomialDist(n, p, A34, false) → B34
  36. BinomialDist(n, p, A35, false) → B35
  37. BinomialDist(n, p, A36, false) → B36
  38. BinomialDist(n, p, A37, false) → B37
  39. BinomialDist(n, p, A38, false) → B38
  40. BinomialDist(n, p, A39, false) → B39
  41. BinomialDist(n, p, A40, false) → B40
  42. BinomialDist(n, p, A41, false) → B41
  43. BinomialDist(n, p, A42, false) → B42
  44. BinomialDist(n, p, A43, false) → B43
  45. BinomialDist(n, p, A44, false) → B44
  46. BinomialDist(n, p, A45, false) → B45
  47. BinomialDist(n, p, A46, false) → B46
  48. BinomialDist(n, p, A47, false) → B47
  49. BinomialDist(n, p, A48, false) → B48
  50. BinomialDist(n, p, A49, false) → B49
  51. BinomialDist(n, p, A50, false) → B50
  52. BinomialDist(n, p, A51, false) → B51
  53. BinomialDist(n, p, A52, false) → B52
  54. BinomialDist(n, p, A53, false) → B53
  55. BinomialDist(n, p, A54, false) → B54
  56. BinomialDist(n, p, A55, false) → B55
  57. BinomialDist(n, p, A56, false) → B56
  58. BinomialDist(n, p, A57, false) → B57
  59. BinomialDist(n, p, A58, false) → B58
  60. BinomialDist(n, p, A59, false) → B59
  61. BinomialDist(n, p, A60, false) → B60
  62. BinomialDist(n, p, A61, false) → B61
  63. BinomialDist(n, p, A62, false) → B62
  64. BinomialDist(n, p, A63, false) → B63
  65. BinomialDist(n, p, A64, false) → B64
  66. BinomialDist(n, p, A65, false) → B65
  67. BinomialDist(n, p, A66, false) → B66
  68. BinomialDist(n, p, A67, false) → B67
  69. BinomialDist(n, p, A68, false) → B68
  70. BinomialDist(n, p, A69, false) → B69
  71. BinomialDist(n, p, A70, false) → B70
  72. BinomialDist(n, p, A71, false) → B71
  73. BinomialDist(n, p, A72, false) → B72
  74. BinomialDist(n, p, A73, false) → B73
  75. BinomialDist(n, p, A74, false) → B74
  76. BinomialDist(n, p, A75, false) → B75
  77. BinomialDist(n, p, A76, false) → B76
  78. BinomialDist(n, p, A77, false) → B77
  79. BinomialDist(n, p, A78, false) → B78
  80. BinomialDist(n, p, A79, false) → B79
  81. BinomialDist(n, p, A80, false) → B80
  82. BinomialDist(n, p, A81, false) → B81
  83. BinomialDist(n, p, A82, false) → B82
  84. BinomialDist(n, p, A83, false) → B83
  85. BinomialDist(n, p, A84, false) → B84
  86. BinomialDist(n, p, A85, false) → B85
  87. BinomialDist(n, p, A86, false) → B86
  88. BinomialDist(n, p, A87, false) → B87
  89. BinomialDist(n, p, A88, false) → B88
  90. BinomialDist(n, p, A89, false) → B89
  91. BinomialDist(n, p, A90, false) → B90
  92. BinomialDist(n, p, A91, false) → B91
  93. BinomialDist(n, p, A92, false) → B92
  94. BinomialDist(n, p, A93, false) → B93
  95. BinomialDist(n, p, A94, false) → B94
  96. BinomialDist(n, p, A95, false) → B95
  97. BinomialDist(n, p, A96, false) → B96
  98. BinomialDist(n, p, A97, false) → B97
  99. BinomialDist(n, p, A98, false) → B98
  100. BinomialDist(n, p, A99, false) → B99
  101. BinomialDist(n, p, A100, false) → B100
  102. BinomialDist(n, p, A101, false) → B101
  103. BinomialDist(n, p, A102, false) → B102
  104. BinomialDist(n, p, A103, false) → B103
  105. BinomialDist(n, p, A104, false) → B104
  106. BinomialDist(n, p, A105, false) → B105
  107. BinomialDist(n, p, A106, false) → B106
  108. BinomialDist(n, p, A107, false) → B107
  109. BinomialDist(n, p, A108, false) → B108
  110. BinomialDist(n, p, A109, false) → B109
  111. BinomialDist(n, p, A110, false) → B110
  112. BinomialDist(n, p, A111, false) → B111
  113. BinomialDist(n, p, A112, false) → B112
  114. BinomialDist(n, p, A113, false) → B113
  115. BinomialDist(n, p, A114, false) → B114
  116. Sequence((k, BinomialDist[n, p, k, true]), k, 0, n) → l4
  117. Sequence((k + 1, BinomialDist[n, p, k, true]), k, 0, n) → l5
  118. Sequence(Segment[(k, BinomialDist[n, p, k, true]), (k + 1, BinomialDist[n, p, k, true])], k, 0, n) → l6

AI Drawing Prompt Reference

Create an interactive binomial probability distribution diagram with four input fields on the left side for entering the number of trials n, success probability p, lower bound l, and upper bound u. In the main coordinate area, generate a series of rectangular bar charts representing the binomial probability mass function from x=0 to x=n, with bars from l to u displayed in a highlighted color. Overlay a smooth normal approximation curve on the same axes using the mean and standard deviation of the binomial distribution as parameters. The entire visualization should update dynamically when users modify the n, p, l, or u values.
The prompt above was compiled from the original drawing commands and is for reference only.