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Date November 2015 Marks available 9 Reference code 15N.3sp.hl.TZ0.3
Level HL only Paper Paper 3 Statistics and probability Time zone TZ0
Command term Calculate Question number 3 Adapted from N/A

Question

Two students are selected at random from a large school with equal numbers of boys and girls. The boys’ heights are normally distributed with mean 178 cm and standard deviation 5.2 cm, and the girls’ heights are normally distributed with mean 169 cm and standard deviation 5.4 cm.

Calculate the probability that the taller of the two students selected is a boy.

Markscheme

let X denote boys’ height and Y denote girls’ height

if BB, P(taller is boy)=1     (A1)

if GG, P(taller is boy)=0     (A1)

if BG or GB:

consider XY     (M1)

E(XY)=178169=9     A1

Var(XY)=5.22+5.42(=56.2)     (M1)A1

P(XY>0)=0.885     A1

answer is 14×1+12×0.885=0.693     (M1)A1

[9 marks]

Examiners report

[N/A]

Syllabus sections

Topic 7 - Option: Statistics and probability » 7.4 » A linear combination of independent normal random variables is normally distributed. In particular, X ~ N(μ,σ2)ˉX ~ N(μ,σ2n) .

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