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Date	May 2018	Marks available	1	Reference code	18M.3.AHL.TZ0.Hsp_1
Level	Additional Higher Level	Paper	Paper 3	Time zone	Time zone 0
Command term	Find	Question number	Hsp_1	Adapted from	N/A

Question

The weights, X kg, of the males of a species of bird may be assumed to be normally distributed with mean 4.8 kg and standard deviation 0.2 kg.

The weights, Y kg, of female birds of the same species may be assumed to be normally distributed with mean 2.7 kg and standard deviation 0.15 kg.

Find the probability that a randomly chosen male bird weighs between 4.75 kg and 4.85 kg.

[1]

Find the probability that the weight of a randomly chosen male bird is more than twice the weight of a randomly chosen female bird.

[6]

Two randomly chosen male birds and three randomly chosen female birds are placed on a weighing machine that has a weight limit of 18 kg. Find the probability that the total weight of these five birds is greater than the weight limit.

[4]

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

Note: In question 1, accept answers that round correctly to 2 significant figures.

P(4.75 < X < 4.85) = 0.197 A1

[1 mark]

Note: In question 1, accept answers that round correctly to 2 significant figures.

consider the random variable X − 2Y (M1)

E(X − 2Y) = − 0.6 (A1)

Var(X − 2Y) = Var(X) + 4Var(Y) (M1)

= 0.13 (A1)

X − 2Y ∼ N(−0.6, 0.13)

P(X − 2Y > 0) (M1)

= 0.0480 A1

[6 marks]

Note: In question 1, accept answers that round correctly to 2 significant figures.

let W = X₁ + X₂ + Y₁ + Y₂ + Y₃ be the total weight

E(W) = 17.7 (A1)

Var(W) = 2Var(X) + 3Var(Y) = 0.1475 (M1)(A1)

W ∼ N(17.7, 0.1475)

P(W > 18) = 0.217 A1

[4 marks]

Examiners report

[N/A]

Syllabus sections

Topic 4—Statistics and probability » AHL 4.14—Linear transformation of a single RV, E(X) and VAR(X), unbiased estimators

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Topic 4—Statistics and probability

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