Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

A builders’ merchant deals in stones of varying sizes.
(a)[3]

For size $A$ stones, the masses have standard deviation $6$ grams. The mean mass of a random sample of $200$ size $A$ stones is $45$ grams. Find a $95\%$ confidence interval for the population mean mass of size $A$ stones.

(b)[4]

For size $B$ stones, the masses have standard deviation $11$ grams. From a random sample of size $200$, an $\alpha\%$ confidence interval for the population mean mass is obtained with width $4$ grams. Find $\alpha$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Confidence interval written correctly as $45 \pm z\frac{6}{\sqrt{200}}$

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