The Normal Approximation to the Binomial Distribution (VCE SSCE Mathematical Methods): Quizzes

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The Normal Approximation to the Binomial Distribution
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When is the normal approximation to the binomial particularly valuable?

When dealing with large sample sizes

What two parameters determine the shape of a binomial distribution?

Number of trials nn and probability pp

When is a binomial distribution skewed (asymmetric)?

When nn is small and pp is close to 0 or 1

What happens to binomial distributions as nn increases?

They resemble a bell-shaped curve

What is the mean of the approximating normal distribution?

μ=np\mu = np

What is the standard deviation of the approximating normal distribution?

σ=np(1p)\sigma = \sqrt{np(1-p)}

What value must both npnp and n(1p)n(1-p) exceed for the normal approximation to be satisfactory?

5

When does the normal approximation work best regarding pp?

When pp is not too close to 0 or 1

How do the parameters of the approximating normal compare to the original binomial?

They are exactly the same

What ensures the binomial distribution is symmetric enough for normal approximation?

Both npnp and n(1p)n(1-p) exceed 5

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