CAIE A-Level Mathematics 6.2 Linear Combinations of Random Variables

CAIE A-Level Mathematics 6.2 Linear Combinations of Random Variables
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise forming distributions for sums, differences and scaled independent normal variables before calculating probabilities.

Exam points

  • combine means linearly but add squared-coefficient variances for independent variables
  • translate a contextual comparison into one linear combination before standardising
  • use the derived mean and standard deviation to calculate the required probability

Covered syllabus points

6.2.1—Normal distribution

Question 6

[Maximum number: 10]

The masses, in kilograms, of large and small bags of potatoes have the independent distributions N(2.5,0.05) and N(0.8,0.02) respectively.

Question 6(a)

(a)

Find the probability that the total mass of a randomly chosen large bag of potatoes and a randomly chosen small bag of potatoes is more than 3.55 kg .

[ 5 ]

Question 6(b)

(b)

Find the probability that the mass of a randomly chosen large bag of potatoes is less than 3 times the mass of a randomly chosen small bag of potatoes.

[ 5 ]