The volumes, in millilitres, of large and small cups of tea are modelled by the distributions $$\(\mathrm{N}(200,30)\)$$ and $$\(\mathrm{N}(110,20)\)$$ respectively. Find the probability that the total volume of a randomly chosen large cup of tea and a randomly chosen small cup of tea is less than $$\(300 \mathrm{ml}\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m20_qp_62 Year：2020 Question No：6(a)
Answer:
\(\mathrm{N}(310,50)\)
\(\frac{300-' 310^{\prime}}{\sqrt{5^{\prime} 0^{\prime}}}(=-1.414)\)
\(\Phi\left({ }^{\prime}-1.414^{\prime}\right)=1-\phi\left({ }^{\prime} 1.414^{\prime}\right)\)
\(=0.0786\) or \(0.0787(3 \mathrm{sf})\)
\(\frac{300-' 310^{\prime}}{\sqrt{5^{\prime} 0^{\prime}}}(=-1.414)\)
\(\Phi\left({ }^{\prime}-1.414^{\prime}\right)=1-\phi\left({ }^{\prime} 1.414^{\prime}\right)\)
\(=0.0786\) or \(0.0787(3 \mathrm{sf})\)
Knowledge points:
6.2.1.5 if X and Y have independent normal distributions then aX + bY has a normal distribution
Solution:
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