A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2025 · Q36 Marks
The data produced by a certain data entry firm always include a small number of incorrect characters that occur at random. The proportion of incorrect characters is denoted by p, and experience has shown that p = 0.0001. A particular data set from the firm contains 14500 characters, of which X characters are incorrect.
- (a)Use a suitable approximating distribution to find P(X < 4).[3]
- (b)The firm's management wishes to decrease the value of p by giving their employees some training. Their aim is that, for a data set containing 14500 characters, the value of P(X = 0) for the new value of p should be double the value of P(X = 0) when p = 0.0001. Use a suitable approximating distribution to find the new value of p.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- B1 Need indication of Poisson.
- M1 Allow one term extra or omitted or incorrect. Allow incorrect lambda.
- A1 SC use of Binomial(14500, 0.0001) to find prob (< 4) = 0.940485 = 0.940 scores B2. Unjustified 0.94[0] or 0.941scores B1B1.
- B1FT FT their λ from 3(a).
- M1 Forming an equation in p and attempting to solve. FT their e-14500P. Factor of 2 on the wrong side of the equation can still score M1.
- A1 OE. Use of binomial reaching 0.0000522 scores SCB2.
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