What are the mean and standard deviation for the normal approximation to the binomial distribution with n = 100 and p = .20?
A)µ = 50 and σ = 5
B)µ = 50 and σ = 4
C)µ = 20 and σ = 16
D)µ = 20 and σ = 4

Question

What are the mean and standard deviation for the normal approximation to the binomial distribution with n = 100 and p = .20?​
A)​µ = 50 and σ = 5
B)​µ = 50 and σ = 4
C)​µ = 20 and σ = 16
D)​µ = 20 and σ = 4

Quizplus · Accepted Answer

The formula for mean (µ) and standard deviation (σ) of the normal approximation to the binomial distribution is:
µ = np
σ = √(np(1-p))

Using n = 100 and p = 0.20, we get:
µ = 100 * 0.20 = 20
σ = √(100 * 0.20 * 0.80) = 4

Therefore, the correct choice is D, with a mean of 20 and a standard deviation of 4.

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