Quick questions on Sample proportions and sampling distributions: VCE Math Methods Unit 4

6short 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 conditions for the formula?

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These are the conditions of the binomial distribution:

X \sim \text{Bin}(n, p)

What is wrong formula for SD?

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\sqrt{p (1 - p) / n}

, not

\sqrt{p (1 - p) n}

\sqrt{p / n}

. The factor of

n

is in the denominator.

What is calculator without set-up?

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Paper 2 expects the explicit standardisation set-up. A naked normCdf call without the distribution statement loses set-up marks.

What is q1?

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A population has

p = 0.3

. For a sample of

n = 100

, find the mean and standard deviation of

\hat{p}

. [2 marks]

What is q2?

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For

p = 0.5

and

n = 100

, find

P(\hat{p} > 0.6)

using the normal approximation. [3 marks]

What is q3?

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Find the smallest

n

so that

\text{SD}(\hat{p}) < 0.03

when

p = 0.4

. [3 marks]

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