A-LevelMathematicsProbability and statistics9709/61 · May/June 2023 · Q16 Marks

In a certain country, 20540 adults out of a population of 6012300 have a degree in medicine.

(a)Use an approximating distribution to calculate the probability that, in a random sample of 1000 adults in this country, there will be fewer than 4 adults who have a degree in medicine.[4]
(b)Justify the approximating distribution used in part (a).[2]

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

[B1] 20540/6012300 = 0.0034163
[B1] Po(3.4163) (Could be implied by expression seen.)
[M1] e-their '3.4163'(1 + 3.4163 + 3.4163^2/2! + 3.4163^3/3!) OR e-their '3.4163'(1 + 3.4163 + 5.8356+6.6453) or 0.03283 + 0.1122 +0.1916+ 0.21819) (Allow any λ. Allow with one end error. Must see expression.)
[A1] = 0.555 (3sf) (CAO. SC No working: B1 B1 (Po must be stated) B1 correct answer (max 3/4). SC Binomial: B1 B0 B1 correct answer (max 2/4).)
[B1] n = 1000 > 50 (Must show comparison with 50.)
[B1] np = 3.4163 <5 (Must show comparison with 5. SC B1: n > 50 (or n large), np < 5. SC B1: n large, p small.)

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, May/June 2023 Paper 6 Variant 1, question 1.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content