The random variable $X$ follows the normal distribution $\mathrm { N } \left( 10,2 ^ { 2 } \right)$, and the random variable $Y$ follows the normal distribution $\mathrm { N } \left( m , 2 ^ { 2 } \right)$. The probability density functions of $X$ and $Y$ are $f ( x )$ and $g ( x )$ respectively.
$$f ( 12 ) \leq g ( 20 )$$
For $m$ satisfying this condition, what is the maximum value of $\mathrm { P } ( 21 \leq Y \leq 24 )$ using the standard normal distribution table on the right? [4 points]
| $z$ | $\mathrm { P } ( 0 \leq Z \leq z )$ |
| 0.5 | 0.1915 |
| 1.0 | 0.3413 |
| 1.5 | 0.4332 |
| 2.0 | 0.4772 |
(1) 0.5328
(2) 0.6247
(3) 0.7745
(4) 0.8185
(5) 0.9104