Question

Assume a binomial distribution where n = 5 and pi = .30

a. Refer to Appendix B.1 and list the probabilities for values of x from 0 to 5. (Round your answers to 3 decimal places)

b. Determine the mean and standard deviation of the distribution from the general definitions given in formulas (6 - 1) and (6 - 2). (Round your mean value to 2 decimal places and standard deviation value to 3 decimal places.)

Answer 1

n = 5

p = 0.3

P(X = x) = 5Cx * 0.3^x * (1 - 0.3)^5-x

a) P(X = 0) = 5C0 * 0.3⁰ * 0.7⁵ = 0.168

P(X = 1) = 5C1 * 0.3¹ * 0.7⁴ = 0.360

P(X = 2) = 5C2 * 0.3² * 0.7³ = 0.309

P(X = 3) = 5C3 * 0.3³ * 0.7² = 0.132

P(X = 4) = 5C4 * 0.3⁴ * 0.7¹ = 0.02

P(X = 5) = 5C5 * 0.3⁵ * 0.7⁰ = 0.002

b) Mean = n * p = 5 * 0.3 = 1.5

Standard deviation = sqrt(n * p * (1 - p)) = sqrt(5 * 0.3 * 0.7) = 1.025