A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2019 · Q48 Marks

In Quarendon, 66% of households are satisfied with the speed of their wifi connection.

(i)Find the probability that, out of 10 households chosen at random in Quarendon, at least 8 are satisfied with the speed of their wifi connection.[3]
(ii)A random sample of 150 households in Quarendon is chosen. Use a suitable approximation to find the probability that more than 84 are satisfied with the speed of their wifi connection.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[M1] Correct binomial term, ¹⁰Ca 0.66º(1−0.66)ᵇ a+b=10, 0<a,b<10
[A1] Correct unsimplified expression
[B1] CAO 0.284
[B1] Accept evaluated or unsimplified μ, σ² numerical expressions, condone σ= √33.66 = 5.8017 or 5.802 CAO np = 0.66×150 = 99 npq = 0.66×(1-0.66)×150 = 33.66
[M1] + Standardise, (x - their 99) / (√their 33.66) condone o², x a value
[M1] 84.5 or 83.5 used in their standardisation formula
[M1] Correct final area
[A1] Final answer (accept 0.9938) SC if no standardisation formula seen, B2 P(Z > -2.499) = 0.994

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source: A-Level Mathematics, Oct/Nov 2019 Paper 6 Variant 2, question 4.

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