A binomial distribution has 100 trials (n = 100)with a probability of success of 0.25 (π = 0.25). To apply the normal distribution to approximate the binomial,what are the mean and standard deviation?
A)µ= 100 and σ = 0.25
B)µ = 25 and σ = 100
C)µ = 25 and σ = 4.33
D)µ= 100 and σ = 2500

Question

Quizplus · Accepted Answer

To approximate the binomial distribution with a normal distribution, we need to use the mean (µ) and standard deviation (σ) of the normal distribution. The mean of the binomial distribution is µ = nπ = 100(0.25) = 25. The variance of the binomial distribution is σ^2 = nπ(1-π) = 100(0.25)(0.75) = 18.75, so the standard deviation is σ = √(σ^2) = √(18.75) ≈ 4.33. Therefore, the best choice is C, with µ = 25 and σ = 4.33.

A Binomial Distribution Has 100 Trials (N = 100)with a Probability