Binomial probability: P(X = 5) for n = 10, p = 0.5
Compute a binomial point probability and the cumulative tails.
Solution
- Distribution X ~ Binomial(n = 10, p = 0.5)
- P(X = k) C(10, 5)·0.5^5·0.5^5 = 0.246094
- P(X ≤ k) 0.623047
- P(X < k) 0.376953
- P(X ≥ k) 1 − P(X < k) = 0.623047
- P(X > k) 0.376953
- Mean μ = n·p = 5
- Variance σ² = n·p·(1 − p) = 2.5
- Standard deviation σ = 1.58114
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