Normal Approximation of Binomial (Edexcel A-Level Mathematics): Quizzes

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Normal Approximation of Binomial Distribution
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When is Normal approximation to the Binomial distribution most useful?

When dealing with a large number of trials

What is one probability condition for using Normal approximation to Binomial?

np≥5np \geq 5

Which two conditions must both be met for Normal approximation?

np≥5np \geq 5 and n(1−p)≥5n(1-p) \geq 5

Why are the probability conditions needed for Normal approximation?

To ensure Binomial is bell-shaped enough

What is the mean (μ\mu) when approximating Binomial with Normal?

npnp

What is the standard deviation (σ\sigma) for Normal approximation of Binomial?

np(1−p)\sqrt{np(1-p)}

Why is a continuity correction needed?

Normal is continuous, Binomial is discrete

By how much do we adjust bounds when applying continuity correction?

0.50.5

To find P(65≤X≤75)P(65 \leq X \leq 75) in Binomial, what is used in Normal?

P(64.5<X<75.5)P(64.5 < X < 75.5)

What formula converts adjusted values to z-scores?

Z=x−μσZ = \frac{x - \mu}{\sigma}

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