A random variable is binomially distributed with n = 16 and π = .40. The expected value and standard deviation of the variables are:
A)2.00 and 1.24
B)4.80 and 4.00
C)6.40 and 1.96
D)2.00 and 1.20

Question

Quizplus · Accepted Answer

The expected value of a binomial distribution is given by E(X) = nπ. Therefore, E(X) = 16(.4) = 6.4.

The standard deviation of a binomial distribution is given by σ = √(nπ(1-π)). Therefore, σ = √(16(.4)(.6)) = 1.96.

The closest option to these values is choice C. Choice A has the correct expected value, but the standard deviation is incorrect. Choice B has the correct standard deviation, but the expected value is too high. Choice D has an incorrect standard deviation.

A Random Variable Is Binomially Distributed with N = 16