A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2018 · Q810 Marks
The results of a survey at a certain large college show that the proportion of students who own a car is 1/4.
- (i)Five students at the college are chosen at random. Find the probability that at least four of these students own a car.[3]
- (ii)For a random sample of n students at the college, the probability that at least one of the students owns a car is greater than 0.995. Find the least possible value of n.[3]
- (iii)For a random sample of 160 students at the college, use a suitable approximate distribution to find the probability that fewer than 50 own a car.[4]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2018). The mark or mark type is shown in brackets.
- [M1] One binomial term, with p < 1, n=5, p + q=1
- [M1] Add 2 correct unsimplified binomial terms
- [A1]
- [M1] Equation or inequality involving 0.75ⁿ and 0.005 or 0.25ⁿ and 0.995
- [M1] Attempt to solve their exponential equation using logs, or trial and error
- [A1] May be implied by their answer
- [B1] Correct unsimplified mean and variance
- [M1] Use standardisation formulae must include square root.
- [M1] Use continuity correction ±0.5 (49.5 or 50.5)
- [A1] Correct final answer
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