Question

In a binomial distribution, n = 7 and π=0.24π=0.24 . Find the probabilities of the following events. (Round your answers to 4 decimal places.)

a.	x=2x

b.	x≤2x

c.	x≥3x

Answer 1

p = 0.24

n = 7

P(X = x) = 7Cx * 0.24^x * (1 - 0.24)^7-x

a) P(X = 2) = 7C2 * 0.24² * 0.76⁵ = 0.3067

b) P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2)

                  = 7C0 * 0.24⁰ * 0.76⁷ + 7C1 * 0.24¹ * 0.76⁶ + 7C2 * 0.24² * 0.76⁵

                  = 0.7769

c) P(X > 3) = 1 - P(X < 3) = 1 - P(X < 2) = 1 - 0.7769 = 0.2231