A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2019 · Q611 Marks

The results of a survey by a large supermarket show that 35% of its customers shop online.

(i)Six customers are chosen at random. Find the probability that more than three of them shop online.[3]
(ii)For a random sample of n customers, the probability that at least one of them shops online is greater than 0.95. Find the least possible value of n.[3]
(iii)For a random sample of 100 customers, use a suitable approximating distribution to find the probability that more than 39 shop online.[5]

Mark scheme

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

[M1] Binomial term of form ⁶Cₓpˣ(1-p)⁶⁻ˣ 0 < p < 1 any p, x ≠ 6,0
[A1] Correct unsimplified answer
[A1]
[M1] Equation or inequality involving ‘0.65ⁿ or 0.35ⁿ’ and ‘0.95 or 0.05’
[M1] Attempt to solve their exponential equation using logs or Trial and Error.
[A1] CAO
[B1] Correct unsimplified np and npq,
[M1] Substituting their µ and σ (condone σ²) into the ±Standardisation Formula with a numerical value for ‘39.5’.
[M1] Using continuity correction 39.5 or 40.5
[M1] Appropriate area Φ from standardisation formula P(z>....) in final solution, (>0.5 if z is -ve, <0.5 if z is +ve)
[A1] Final answer

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