A random variable $X$ follows a normal distribution $\mathrm { N } \left( m , \sigma ^ { 2 } \right)$ and satisfies the following conditions.
(a) $\mathrm { P } ( X \geq 64 ) = \mathrm { P } ( X \leq 56 )$
(b) $\mathrm { E } \left( X ^ { 2 } \right) = 3616$ What is the value of $\mathrm { P } ( X \leq 68 )$ obtained using the table on the right? [3 points]
(1) 0.9104
(2) 0.9332
(3) 0.9544
(4) 0.9772
(5) 0.9938
| $x$ | $\mathrm { P } ( m \leq X \leq x )$ |
| $m + 1.5 \sigma$ | 0.4332 |
| $m + 2 \sigma$ | 0.4772 |
| $m + 2.5 \sigma$ | 0.4938 |