두 과목 정규분포

$\mathrm{A}$과목 점수 $X \sim N ( m , \sigma ^{2} )$ $\mathrm{B}$과목 점수 $Y \sim N ( m + 3 , \sigma ^{2} )$ $\displaystyle {\mathrm{P}} ( X \geq 80 ) = {\mathrm{P}} \left( Z \geq \frac{80 - m}{\sigma} \right) = 0.09$에서 $\displaystyle {\mathrm{P}} \left( 0 \leq z \leq \frac{80 - m}{\sigma} \right) = 0.41$ $\displaystyle {\mathrm{P}} ( Y \geq 80 ) = {\mathrm{P}} \left( Z \geq \frac{80 - m - 3}{\sigma} \right) = 0.15$에서 $\displaystyle {\mathrm{P}} \left( 0 \leq z \leq \frac{80 - m - 3}{\sigma} \right) = 0.35$ ${\mathrm{P}} \left( 0 \leq z \leq 1.34 \right) = 0.41$, ${\mathrm{P}} \left( 0 \leq z \leq 1.04 \right) = 0.35$이므로 $\displaystyle \frac{80 - m}{\sigma} = 1.34$, $\displaystyle \frac{80 - m - 3}{\sigma} = 1.04$ 두 식을 연립하여 풀면 $\sigma = 10 , m = 66.6$이다. 따라서 $m + \sigma = 76.6$