A population follows a normal distribution $\mathrm { N } \left( m , 2 ^ { 2 } \right)$. Let $\overline { X _ { A } }$ and $\overline { X _ { B } }$ be the sample means of samples of size 7 and size 10, respectively, drawn from this population. Using the distributions of $\overline { X _ { A } }$ and $\overline { X _ { B } }$, the 95\% confidence intervals for the population mean $m$ are $[a, b]$ and $[c, d]$, respectively. Choose all correct statements from the given options. [4 points] Options ㄱ. The variance of $\overline { X _ { A } }$ is greater than the variance of $\overline { X _ { B } }$. ㄴ. $\mathrm { P } \left( \overline { X _ { A } } \leqq m + 2 \right) < \mathrm { P } \left( \overline { X _ { B } } \leqq m + 2 \right)$ ㄷ. $d - c < b - a$ (1) ㄱ (2) ㄷ (3) ㄱ, ㄴ (4) ㄴ, ㄷ (5) ㄱ, ㄴ, ㄷ
A population follows a normal distribution $\mathrm { N } \left( m , 2 ^ { 2 } \right)$. Let $\overline { X _ { A } }$ and $\overline { X _ { B } }$ be the sample means of samples of size 7 and size 10, respectively, drawn from this population. Using the distributions of $\overline { X _ { A } }$ and $\overline { X _ { B } }$, the 95\% confidence intervals for the population mean $m$ are $[a, b]$ and $[c, d]$, respectively. Choose all correct statements from the given options. [4 points]
\textbf{Options}\\
ㄱ. The variance of $\overline { X _ { A } }$ is greater than the variance of $\overline { X _ { B } }$.\\
ㄴ. $\mathrm { P } \left( \overline { X _ { A } } \leqq m + 2 \right) < \mathrm { P } \left( \overline { X _ { B } } \leqq m + 2 \right)$\\
ㄷ. $d - c < b - a$\\
(1) ㄱ\\
(2) ㄷ\\
(3) ㄱ, ㄴ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ