The masses, in kilograms, of large and small sacks of flour have the distributions $$\(N\left(55,3^{2}\right)\)$$ and $$\(\mathrm{N}\left(27,2.5^{2}\right)\)$$ respectively. Some sacks are loaded onto a boat. The maximum load of flour that the boat can carry safely is $$\(340 \mathrm{~kg}\)$$. Find the probability that the boat can carry safely 3 randomly chosen large sacks of flour and 6 randomly chosen small sacks of flour. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s21_qp_61 Year：2021 Question No：7(a)
Answer:
\(\mathrm{E}(T)=3 \times 55+6 \times 27[=327]\)
\(\operatorname{Var}(T)=3 \times 3^{2}+6 \times 2.5^{2}[=64.5]\)
\(\frac{340-' 327^{\prime}}{\sqrt{{ }^{\prime} 64.5^{\prime}}}[=1.619]\)
\(\mathrm{P}\left(z<^{\prime} 1.619^{\prime}\right)=\Phi\left(' 1.619^{\prime}\right)\)
\(0.947(3 \mathrm{sf})\)
\(\operatorname{Var}(T)=3 \times 3^{2}+6 \times 2.5^{2}[=64.5]\)
\(\frac{340-' 327^{\prime}}{\sqrt{{ }^{\prime} 64.5^{\prime}}}[=1.619]\)
\(\mathrm{P}\left(z<^{\prime} 1.619^{\prime}\right)=\Phi\left(' 1.619^{\prime}\right)\)
\(0.947(3 \mathrm{sf})\)
Knowledge points:
6.2.1.2 more contents
6.2.1.3 more contents
6.2.1.5 if X and Y have independent normal distributions then aX + bY has a normal distribution
Solution:
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