A-LevelMathematicsProbability and statistics9709/61 · May/June 2024 · Q36 Marks

The time taken in minutes for a certain daily train journey has a normal distribution with standard deviation 5.8. For a random sample of 20 days the journey times were noted and the mean journey time was found to be 81.5 minutes.

(a)Calculate a 98% confidence interval for the population mean journey time.[3]
(b)A student was asked for the meaning of this confidence interval. The student replied as follows. 'The times for 98% of these journeys are likely to be within the confidence interval.' Explain briefly whether this statement is true or not.[1]
(c)Two independent 98% confidence intervals are found. Given that at least one of these intervals contains the population mean, find the probability that both intervals contain the population mean.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

[M1] 81.5 ± z x 5.8/√20
[B1] z = 2.326
[A1] 78.5 to 84.5 (3sf)
[B1] Not true. C. I. is for mean time, not individual times. Both comments needed.
[M1] 0.98^2 / (1-0.02^2)
[A1] = 0.961 (3sf)

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About this question

Topic

Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.

Source

A-Level Mathematics, May/June 2024 Paper 6 Variant 1, question 3.

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