Mathematics 9709/62 — October/November 2022

Cambridge A-Level · Probability & Statistics 2 · worked solutions for every part, with the mark scheme

questions

marks

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Topics Sampling and Estimation · Hypothesis Tests · The Poisson Distribution · Linear Combinations of Random Variables · Continuous Random Variables

Q1Sampling and EstimationFree sample

Each of a random sample of 80 adults gave an estimate, $h$ metres, of the height of a particular building. The results were summarised as follows.

n = 80 \quad \sum h = 2048 \quad \sum h^2 = 52\,760

(a)

Calculate unbiased estimates of the population mean and variance.

(b)

Using this sample, the upper boundary of an $\alpha\%$ confidence interval for the population mean is 26.0.

Find the value of $\alpha$ .

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