A-LevelMathematicsProbability and statistics9709/61 · May/June 2021 · Q24 Marks
The time, in minutes, taken by students to complete a test has the distribution N(125, 36).
- (a)Find the probability that the mean time taken to complete the test by a random sample of 40 students is less than 123 minutes.[3]
- (b)Explain whether it was necessary to use the Central Limit theorem in the solution to part (a).[1]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [M1] `123-125 / (6/√40)` [= -2.108...]
- [M1] Must have √40. No standard deviation/variance mix. Ignore any continuity correction attempts for this mark. For correct probability area consistent with their working.
- [A1] = 0.0175 or 0.0176 (3 sf)
- [B1] No, population is normal. Need both.
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