3.
\((1)\)公共汽车车门高度是按男子与车门碰头机会不高于\(0.0228\)来设计的\(.\)设男子身高\(X\)服从正态分布\(N(170,{{7}^{2}})(\)单位:\(cm)\),参考以下概率
\(P(\mu -\sigma < X\leqslant \mu +\sigma )=0.6826\),\(P(\mu -2\sigma < X\leqslant \mu +2\sigma )=0.9544\),\(P(\mu -3\sigma < X\leqslant \mu +3\sigma )=0.9974\)
则车门的高度\((\)单位:\(cm)\)至少应设计为______________ \(.\)
\((2)\) \(\left( 1+ax \right){{\left( 1+x \right)}^{5}}\)的展开式中\({{x}^{2}}\)的系数是\(5\),则\(a=\)_________.
\((3)\)从标有\(1\),\(2\),\(3\),\(4\),\(5\)的五张卡片中,依次抽出\(2\)张,则在第一次抽到偶数的条件下,第二次抽到奇数的概率为_________\(.\)
\((4)\)若二项式\({{\left( \dfrac{\sqrt{5}}{5}{{x}^{2}}+\dfrac{1}{x} \right)}^{6}}\)的展开式中的常数项为\(m\),则\(\int_{1}^{m}{{{x}^{2}}dx}=\)________\(.\)