A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2021 · Q410 Marks
On average, 1 in 400 microchips made at a certain factory are faulty. The number of faulty microchips in a random sample of 1000 is denoted by X.
- (a)State the distribution of X, giving the values of any parameters.[1]
- (b)State an approximating distribution for X, giving the values of any parameters.[2]
- (c)(i)P(X = 4).[2]
- (c)(ii)P(2 ≤ X ≤ 4).[2]
- (d)Use a suitable approximating distribution to find the probability that, in a random sample of 700 microchips, there will be at least 1 faulty one.[3]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2021). The mark or mark type is shown in brackets.
- [B1] B(1000, 1/400)
- [B2] Po(2.5)
- [M1] e⁻²·⁵ x 2.5⁴ / 4!
- [A1] 0.134 (3 sf)
- [M1] e⁻²·⁵(2.5²/2! + 2.5³/3! + 2.5⁴/4!)
- [A1] 0.604 (3 sf)
- [M1] λ = 2.5 x 0.7 or λ = 700 x 1/400 [= 1.75]
- [M1] 1 - e⁻¹·⁷⁵
- [A1] 0.826
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