A-LevelMathematicsProbability and statistics9709/63 · Oct/Nov 2019 · Q47 Marks
The heights of students at the Mainland college are normally distributed with mean 148 cm and standard deviation 8 cm.
- (i)The probability that a Mainland student chosen at random has a height less than h cm is 0.67. Find the value of h.[3]
- (ii)120 Mainland students are chosen at random. Find the number of these students that would be expected to have a height within half a standard deviation of the mean.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [B1] z = ±0.44 seen
- [M1] z-value = ±(h-148)/8
- [A1] CAO
- [M1] Using ± standardisation formula for either 144 or 152, μ = 148, σ = 8 and no continuity correction, allow σ² or √σ
- [M1] Correct final area legitimately obtained from phi(their z2) - phi(their z1)
- [A1] Final probability answer
- [B1FT] Their prob (to 3 or 4 sf) × 120, rounded to a whole number or truncated
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