Quick questions on Approximating distributions explained: H2 Mathematics Probability and Statistics

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is wrong direction of the correction?

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For

X \geq k

shift down to

k - 0.5

; for

X \leq k

shift up to

k + 0.5

. Sketch to check.

What is wrong variance for the Poisson normal approximation?

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Both the mean and variance equal

\lambda

What is q1?

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State the conditions for approximating the binomial by the Poisson. [2 marks]

What is q2?

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Apply the continuity correction to

\mathrm{P}(X \geq 20)

for a normal approximation. [1 mark]

What is q3?

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For

\mathrm{B}(200, 0.5)

, state the normal approximation's mean and variance. [2 marks]

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