A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2025 · Q77 Marks
The time, in minutes, taken by students to complete a test is modelled by the random variable X with probability density function f(x) = { -3/4(x-3)(x-5) 3 ≤ x ≤ 5, { 0 otherwise.
- (a)Find the probability that a randomly chosen student takes longer than 4.5 minutes to complete the test.[4]
- (b)Write down the median of X.[1]
- (c)Without performing an integration, use your answer to part (a) to find P(3.5 < X < 4.5).[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- M1 Attempt to integrate their f(x). Condone missing -3/4.
- A1 Correct integration and correct limits 4.5 and 5. OE e.g. 1- integration from 3 to 4.5 condone missing -3/4.
- M1 Attempt substitute correct limits in correct integral must have the -3/4. OE. May be implied by correct answer.
- A1
- B1
- M1 Must see working. FT their 5/32.
- A1FT FT their 5/32. SC not using 7(a) and integrating from 3.5 to 4.5 and getting 11/16 OE scores B1 only.
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