A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2021 · Q59 Marks

In a certain large document, typing errors occur at random and at a constant mean rate of 0.2 per page.

(a)Find the probability that there are fewer than 3 typing errors in 10 randomly chosen pages.[2]
(b)Use an approximating distribution to find the probability that there are more than 50 typing errors in 200 randomly chosen pages.[4]
(c)In the same document, formatting errors occur at random and at a constant mean rate of 0.3 per page. Find the probability that the total number of typing and formatting errors in 20 randomly chosen pages is between 8 and 11 inclusive.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[M1] P(X<3) any λ. Allow one end error.
[A1] 0.677 (3sf) Unsupported correct answer scores SC B1 only.
[M1] N(40, 40) SOI
[M1] 50.5-40 / √40 [= 1.660] For standardising with their values. Allow with wrong or no cc must have square root.
[M1] P(z > '1.660') = 1 – Ф(‘1.660') Correct area consistent with their working.
[A1] 0.0485 or 0.0484 (3sf)
[B1] λ = 10 Condone mean 10.
[M1] e^-10 (10^8/8! + 10^9/9! + 10^10/10! + 10^11/11!) Allow any λ (allow one end error).
[A1] 0.477 (3sf) Unsupported correct answer scores SC B2 only.

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