A-LevelMathematicsProbability and statistics9709/62 · May/June 2020 · Q39 Marks

In the data-entry department of a certain firm, it is known that 0.12% of data items are entered incorrectly, and that these errors occur randomly and independently.

(a)(i)A random sample of 3600 data items is chosen. The number of these data items that are incorrectly entered is denoted by X. State the distribution of X, including the values of any parameters.[1]
(a)(ii)State an appropriate approximating distribution for X, including the values of any parameters. Justify your choice of approximating distribution.[3]
(a)(iii)Use your approximating distribution to find P(X > 2).[2]
(b)Another large random sample of n data items is chosen. The probability that the sample contains no data items that are entered incorrectly is more than 0.1. Use an approximating distribution to find the largest possible value of n.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[B1] B(3600, 0.0012)
[B2] Po(4.32) (B1 for Po. B1 for λ = 4.32)
[B1] n = 3600 which is large, p = 0.12% which is small and np = 4.32 which is < 5
[M1] 1-e^-4.32 (1 + 4.32 + 4.32^2 / 2)
[A1] 0.805 (3 sf)
[M1] e^-λ > 0.1
[A1] (−λ > ln0.1) OR (λ < ln10) OR (0.0012n < ln10)
[A1] (n < 1918.8) largest n is 1918

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