u x-u P% M=士1 土0 G u+o P=2×0.3413=0.6826=68.26% u户±2 ±2o u-20 +2G P=2×04773=0.9546=95.46% M=±3 ±3a L-3G +3o P=2×0.4987=0.9974=99.74% <例>按照正态分布x在区间(-0.5o,+1.5o出现的概率 解：根据 =-4 0 可将h0.5o≤≤H1.5o变换为-0.5≤u≤1.5 查表u=0.5时面积为0.1915 u=1.5时面积为0.4332 则-0.5≤u≤1.5的总面积即为x在区间(4-0.5o, 4+1.5o)出现的概率P=0.1915+0.4332=0.6247u x -μ x P % u=±1 ±σ µ-σ µ+σ P=2× 0.3413 = 0.6826 =68.26% u=± 2 ± 2σ µ-2σ µ+2σ P=2× 0.4773 = 0.9546 =95.46% u=± 3 ± 3σ µ-3σ µ+3σ P=2× 0.4987 = 0.9974=99.74% <例> 按照正态分布x在区间(µ-0.5σ, µ+1.5σ)出现的概率 解: 根据 σ x u − µ = 可将 µ-0.5σ ≤x ≤µ+1.5σ 变换为 -0.5≤u ≤1.5 查表 u=0.5 时 面积为0.1915 u=1.5 时 面积为0.4332 则-0.5≤ u ≤1.5的总面积即为x在区间( µ - 0.5σ , µ +1.5σ )出现的概率 P = 0.1915 + 0.4332=0.6247