第 023 题 / 45

设 $X \sim N\left( {\mu ,{\sigma }_{1}^{2}}\right) ,Y \sim N\left( {\mu ,{\sigma }_{2}^{2}}\right)$ ,这两个概率密度曲线 (如图),下列说法正确的是 ( )

A. ${\sigma }_{1} < {\sigma }_{2}$
B. ${\sigma }_{1} = {\sigma }_{2}$
C. 对任意实数 $m > \mu ,P\left( {X \leq m}\right) > P\left( {Y \leq m}\right)$
D. 若 $P\left( {\mu - {k}_{1}{\sigma }_{1} \leq X \leq \mu + {k}_{1}{\sigma }_{1}}\right) > P\left( {\mu - {k}_{2}{\sigma }_{2} \leq Y \leq \mu + {k}_{2}{\sigma }_{2}}\right) ,k_1,k_2 \in {R}^{ + }$ ,则 ${k}_{1} < {k}_{2}$