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13.1: The Binomial Distribution Table for n = 2 to n = 10

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    The Binomial Distribution Table for n = 2 to n = 10

    Binomial Probabilities
    n X p=0.05 p=0.1 p=0.2 p=0.3 p=0.4 p=0.5 p=0.6 p=0.7 p=0.8 p=0.9 p=0.95
    2 0 0.903 0.810 0.640 0.490 0.360 0.250 0.160 0.090 0.040 0.010 0.003
      1 0.095 0.180 0.320 0.420 0.480 0.500 0.480 0.420 0.320 0.180 0.095
      2 0.003 0.010 0.040 0.090 0.160 0.250 0.360 0.490 0.640 0.810 0.903
    3 0 0.857 0.729 0.512 0.343 0.216 0.125 0.064 0.027 0.008 0.001 0.000
      1 0.135 0.243 0.384 0.441 0.432 0.375 0.288 0.189 0.096 0.027 0.007
      2 0.007 0.027 0.096 0.189 0.288 0.375 0.432 0.441 0.384 0.243 0.135
      3 0.000 0.001 0.008 0.027 0.064 0.125 0.216 0.343 0.512 0.729 0.857
    4 0 0.815 0.656 0.410 0.240 0.130 0.063 0.026 0.008 0.002 0.000 0.000
      1 0.171 0.292 0.410 0.412 0.346 0.250 0.154 0.076 0.026 0.004 0.000
      2 0.014 0.049 0.154 0.265 0.346 0.375 0.346 0.265 0.154 0.049 0.014
      3 0.000 0.004 0.026 0.076 0.154 0.250 0.346 0.412 0.410 0.292 0.171
      4 0.000 0.000 0.002 0.008 0.026 0.063 0.130 0.240 0.410 0.656 0.815
    5 0 0.774 0.590 0.328 0.168 0.078 0.031 0.010 0.002 0.000 0.000 0.000
      1 0.204 0.328 0.410 0.360 0.259 0.156 0.077 0.028 0.006 0.000 0.000
      2 0.021 0.073 0.205 0.309 0.346 0.313 0.230 0.132 0.051 0.008 0.001
      3 0.001 0.008 0.051 0.132 0.230 0.313 0.346 0.309 0.205 0.073 0.021
      4 0.000 0.000 0.006 0.028 0.077 0.156 0.259 0.360 0.410 0.328 0.204
      5 0.000 0.000 0.000 0.002 0.010 0.031 0.078 0.168 0.328 0.590 0.774
    6 0 0.735 0.531 0.262 0.118 0.047 0.016 0.004 0.001 0.000 0.000 0.000
      1 0.232 0.354 0.393 0.303 0.187 0.094 0.037 0.010 0.002 0.000 0.000
      2 0.031 0.098 0.246 0.324 0.311 0.234 0.138 0.060 0.015 0.001 0.000
      3 0.002 0.015 0.082 0.185 0.276 0.313 0.276 0.185 0.082 0.015 0.002
      4 0.000 0.001 0.015 0.060 0.138 0.234 0.311 0.324 0.246 0.098 0.031
      5 0.000 0.000 0.002 0.010 0.037 0.094 0.187 0.303 0.393 0.354 0.232
      6 0.000 0.000 0.000 0.001 0.004 0.016 0.047 0.118 0.262 0.531 0.735
    7 0 0.698 0.478 0.210 0.082 0.028 0.008 0.002 0.000 0.000 0.000 0.000
      1 0.257 0.372 0.367 0.247 0.131 0.055 0.017 0.004 0.000 0.000 0.000
      2 0.041 0.124 0.275 0.318 0.261 0.164 0.077 0.025 0.004 0.000 0.000
      3 0.004 0.023 0.115 0.227 0.290 0.273 0.194 0.097 0.029 0.003 0.000
      4 0.000 0.003 0.029 0.097 0.194 0.273 0.290 0.227 0.115 0.023 0.004
      5 0.000 0.000 0.004 0.025 0.077 0.164 0.261 0.318 0.275 0.124 0.041
      6 0.000 0.000 0.000 0.004 0.017 0.055 0.131 0.247 0.367 0.372 0.257
      7 0.000 0.000 0.000 0.000 0.002 0.008 0.028 0.082 0.210 0.478 0.698
    8 0 0.663 0.430 0.168 0.058 0.017 0.004 0.001 0.000 0.000 0.000 0.000
      1 0.279 0.383 0.336 0.198 0.090 0.031 0.008 0.001 0.000 0.000 0.000
      2 0.051 0.149 0.294 0.296 0.209 0.109 0.041 0.010 0.001 0.000 0.000
      3 0.005 0.033 0.147 0.254 0.279 0.219 0.124 0.047 0.009 0.000 0.000
      4 0.000 0.005 0.046 0.136 0.232 0.273 0.232 0.136 0.046 0.005 0.000
      5 0.000 0.000 0.009 0.047 0.124 0.219 0.279 0.254 0.147 0.033 0.005
      6 0.000 0.000 0.001 0.010 0.041 0.109 0.209 0.296 0.294 0.149 0.051
      7 0.000 0.000 0.000 0.001 0.008 0.031 0.090 0.198 0.336 0.383 0.279
      8 0.000 0.000 0.000 0.000 0.001 0.004 0.017 0.058 0.168 0.430 0.663
    9 0 0.630 0.387 0.134 0.040 0.010 0.002 0.000 0.000 0.000 0.000 0.000
      1 0.299 0.387 0.302 0.156 0.060 0.018 0.004 0.000 0.000 0.000 0.000
      2 0.063 0.172 0.302 0.267 0.161 0.070 0.021 0.004 0.000 0.000 0.000
      3 0.008 0.045 0.176 0.267 0.251 0.164 0.074 0.021 0.003 0.000 0.000
      4 0.001 0.007 0.066 0.172 0.251 0.246 0.167 0.074 0.017 0.001 0.000
      5 0.000 0.001 0.017 0.074 0.167 0.246 0.251 0.172 0.066 0.007 0.001
      6 0.000 0.000 0.003 0.021 0.074 0.164 0.251 0.267 0.176 0.045 0.008
      7 0.000 0.000 0.000 0.004 0.021 0.070 0.161 0.267 0.302 0.172 0.063
      8 0.000 0.000 0.000 0.000 0.004 0.018 0.060 0.156 0.302 0.387 0.299
      9 0.000 0.000 0.000 0.000 0.000 0.002 0.010 0.040 0.134 0.387 0.630
    10 0 0.599 0.349 0.107 0.028 0.006 0.001 0.000 0.000 0.000 0.000 0.000
      1 0.315 0.387 0.268 0.121 0.040 0.010 0.002 0.000 0.000 0.000 0.000
      2 0.075 0.194 0.302 0.233 0.121 0.044 0.011 0.001 0.000 0.000 0.000
      3 0.010 0.057 0.201 0.267 0.215 0.117 0.042 0.009 0.001 0.000 0.000
      4 0.001 0.011 0.088 0.200 0.251 0.205 0.111 0.037 0.006 0.000 0.000
      5 0.000 0.001 0.026 0.103 0.201 0.246 0.201 0.103 0.026 0.001 0.000
      6 0.000 0.000 0.006 0.037 0.111 0.205 0.251 0.200 0.088 0.011 0.001
      7 0.000 0.000 0.001 0.009 0.042 0.117 0.215 0.267 0.201 0.057 0.010
      8 0.000 0.000 0.000 0.001 0.011 0.044 0.121 0.233 0.302 0.194 0.075
      9 0.000 0.000 0.000 0.000 0.002 0.010 0.040 0.121 0.268 0.387 0.315
      10 0.000 0.000 0.000 0.000 0.000 0.001 0.006 0.028 0.107 0.349 0.599
    Table \(\PageIndex{1}\): Binomial Probabilitiy Table for n =2 to n = 10

    This page titled 13.1: The Binomial Distribution Table for n = 2 to n = 10 was last modified on Wed, 20 Aug 2025 23:55:22 GMT and is shared under a Public Domain license and was authored, remixed, and/or curated by Toros Berberyan, Tracy Nguyen, and Alfie Swan.