Probability Theory, Exercise, Solutions, Mathematics.
binomial distribution is given by the formula P(X=k) = nCk × p^k × (1-p)^(n-k), where n=10, k=5, p=0.5. Therefore, P(X=5) = 10C5 × 0.5⁵ × 0.5⁵ ≈ 0.246. (b) The probability for a normal distribution can be determined by standardizing and then consulting a z-table. Calculate Z = (X — μ)/σ, where X =