A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2017 · Q58 Marks
Blank CDs are packed in boxes of 30. The probability that a blank CD is faulty is 0.04. A box is rejected if more than 2 of the blank CDs are faulty.
- (i)Find the probability that a box is rejected.[3]
- (ii)280 boxes are chosen randomly. Use an approximation to find the probability that at least 30 of these boxes are rejected.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- EITHER: (M1 Binomial term of form 30Cxpx(1-p)30-x, 0<p< 1 any p
- A1 Correct unsimplified answer
- A1) = 0.117 (0.116896)
- OR: (M1 Binomial term of form 30Cxpx(1-p)30-x, 0<p< 1 any p
- A1 Correct unsimplified answer
- A1) = 0.117
- M1 FT Correct unsimplified np and npq, FT their p from (i),
- M1 Substituting their µ and σ (√npq only) into the Standardisation Formula
- M1 Using continuity correction of 29.5 or 30.5
- M1 Appropriate area Φ from standardisation formula P(z >....) in final solution
- A1 = 0.726
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