# Given X ~ B(n, P) if n = 25 and E(X) = 10, find p and SD(X). - Mathematics and Statistics

Sum

Given X ~ B(n, P) if n = 25 and E(X) = 10, find p and SD(X).

#### Solution

Given: n = 25 and  E(X) = 10

E(X) = np

∴ 10 = 25 × p

∴ p = 10/25 = 2/5

∴ q = 1 - p = 1 - 2/5 = 3/5

Var(X) = npq

= 25 × 2/5 × 3/5 = 6

∴ SD(X) = sqrt("Var"("X")) = sqrt6

Hence, p = 2/5, S.D.(X) = sqrt6

Concept: Mean of Binomial Distribution (P.M.F.)
Is there an error in this question or solution?