A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2025 · Q44 Marks

The masses of a certain species of animal are known to be normally distributed with standard deviation σkg. A researcher obtains the masses of a random sample of n animals of this species and uses these masses to find two confidence intervals (α% and 90%) for the population mean. The width of the α% confidence interval is 1.414 × the width of the 90% confidence interval.

(a)Find α.[3]
(b)Find the probability that the 90% confidence interval contains the population mean given that the α% confidence interval contains the population mean.[1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

M1 Form an equation in z (accept z = 1.414 × 1.645 OE). Factor of 1.414 on the wrong side of the equation can still score M1. Condone 1.282 instead of 1.645 for M1.
M1 OE.
A1 Allow 98%.
B1FT FT their a. no ft if alpha < 90 in 4(a).

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, Oct/Nov 2025 Paper 6 Variant 1, question 4.

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