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. Find the probability that the mass of a randomly chosen large sack of flour is greater than the total mass of two randomly chosen small sacks of flour. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s21_qp_61 Year：2021 Question No：7(b)
Answer:
\( \mathrm{E}\left(L-S_{1}-S_{2}\right)=55-2 \times 27[=1] \)
\( \operatorname{Var}\left(L-S_{1}-S_{2}\right)=3^{2}+2 \times 2.5^{2}[=21.5] \)
\( \frac{0-1^{\prime} 1^{\prime}}{\sqrt{'^{21.5^{\prime}}}}[=-0.216] \)
\( \mathrm{P}\left(L-S_{1}-S_{2}>0\right)=\Phi\left(' 0.216^{\prime}\right) \)
\( 0.586\quad or\quad 0.585(3 \mathrm{sf}) \)
\( \operatorname{Var}\left(L-S_{1}-S_{2}\right)=3^{2}+2 \times 2.5^{2}[=21.5] \)
\( \frac{0-1^{\prime} 1^{\prime}}{\sqrt{'^{21.5^{\prime}}}}[=-0.216] \)
\( \mathrm{P}\left(L-S_{1}-S_{2}>0\right)=\Phi\left(' 0.216^{\prime}\right) \)
\( 0.586\quad or\quad 0.585(3 \mathrm{sf}) \)
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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