A-LevelMathematicsProbability and statistics9709/62 · May/June 2018 · Q711 Marks

In a certain country, 60% of mobile phones sold are made by Company A, 35% are made by Company B and 5% are made by other companies.

(i)Find the probability that, out of a random sample of 13 people who buy a mobile phone, fewer than 11 choose a mobile phone made by Company A.[3]
(ii)Use a suitable approximation to find the probability that, out of a random sample of 130 people who buy a mobile phone, at least 50 choose a mobile phone made by Company B.[5]
(iii)A random sample of n mobile phones sold is chosen. The probability that at least one of these phones is made by Company B is more than 0.98. Find the least possible value of n.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

[M1] (i) Binomial expression of form ¹³Cₓ (p)ˣ(1-p)¹³⁻ˣ, 0 < x < 13, 0 < p < 1
[M1] (i) Correct unsimplified answer = 1 – ¹³C₁₁(0.6)¹¹(0.4)² – ¹³C₁₂(0.6)¹²(0.4) – (0.6)¹³
[A1] (i) CAO = 0.942
[B1] (ii) Correct unsimplified mean and var (condone σ² = 29.6, σ = 5.438)
[M1] (ii) Standardising, using ±(x - their mean)/σ, x = value to standardise
[M1] (ii) Correct final area = 1 – Ф(0.7355)
[M1] (ii) 1 - 0.7691
[A1] (ii) Correct final answer = 0.231
[M1] (iii) Eqn or inequality involving, 0.65ⁿ and 0.02 or 0.35ⁿ and 0.98
[M1] (iii) Attempt to solve their eqn or inequality by logs or trial and error
[A1] (iii) CAO = 10

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