A-LevelMathematicsProbability and statistics9709/52 · Feb/Mar 2020 · Q58 Marks
In Greenton, 70% of the adults own a car. A random sample of 8 adults from Greenton is chosen.
- (a)Find the probability that the number of adults in this sample who own a car is less than 6.[3]
- (b)A random sample of 120 adults from Greenton is now chosen. Use an approximation to find the probability that more than 75 of them own a car.[5]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.
- M1 One term 8Cx p^x (1-p)^(8-x), 0<p<1, x≠0
- A1 Correct unsimplified expression, or better
- A1
- B1 Correct mean and variance, allow unsimplified
- M1 Substituting their μ and σ into the standardising formula (any number), not σ², not √σ
- M1 Using continuity correction 75.5 or 74.5
- M1 Appropriate area Φ, from final process, must be a probability
- A1 Allow 0.9545 < p < 0.955
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