P(X = 6)
0.205078
20.508%
Probability
Binomial Distribution Calculator
Exact probabilities, tails, range checks, a distribution chart, CSV export, and binomial-test p-values in one worksheet.
P(X = k)P(X <= k)P(X >= k)RangeA/B test
P(X < 6)
0.623047
62.305%
P(X <= 6)
0.828125
82.812%
P(X > 6)
0.171875
17.188%
P(X >= 6)
0.376953
37.695%
Mean
5
Variance
2.5
Std dev
1.5811
Skewness
0
Excess kurtosis
-0.2
Distribution chart
11 outcomes
Distribution table
| k | P(X=k) | P(X<=k) |
|---|---|---|
| 0 | 0.000977 | 0.000977 |
| 1 | 0.009766 | 0.010742 |
| 2 | 0.043945 | 0.054688 |
| 3 | 0.117188 | 0.171875 |
| 4 | 0.205078 | 0.376953 |
| 5 | 0.246094 | 0.623047 |
| 6 | 0.205078 | 0.828125 |
| 7 | 0.117188 | 0.945313 |
| 8 | 0.043945 | 0.989258 |
| 9 | 0.009766 | 0.999023 |
| 10 | 0.000977 | 1 |
Calculation steps
- 1.C(10,6) = 210
- 2.p^k = 0.5^6 = 0.015625
- 3.(1-p)^(n-k) = 0.5^4 = 0.0625
- 4.P(X=6) = C(10,6) x p^k x (1-p)^(n-k) = 0.205078125
Normal approximation
np = 5 and n(1-p) = 5
Exact
0.205078
Normal
0.204524
Error
0.27%
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