A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2018 · Q59 Marks
At the Nonland Business College, all students sit an accountancy examination at the end of their first year of study. On average, 80% of the students pass this examination.
- (i)A random sample of 9 students who will take this examination is chosen. Find the probability that at most 6 of these students will pass the examination.[3]
- (ii)A random sample of 200 students who will take this examination is chosen. Use a suitable approximate distribution to find the probability that more than 166 of them will pass the examination.[5]
- (iii)Justify the use of your approximate distribution in part (ii).[1]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [M1] Any binomial term of form nCx p^x (1 − p)^(n-x), x ≠ 0
- [M1] Correct unsimplified expression
- [A1] Correct answer
- [B1] Both unsimplified
- [M1] Standardise, z = ±(x - their 160)/√(their 32) with square root
- [M1] 166.5 or 165.5 seen in attempted standardisation expression
- [M1] 1-a Φ-value, correct area expression, linked to final answer
- [A1] Correct final answer
- [B1] Both parts required
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