From a population following a normal distribution $\mathrm{N}(m, 5^2)$, a sample of size 49 is randomly extracted, and the sample mean is $\bar{x}$. The 95\% confidence interval for the population mean $m$ is $a \leq m \leq \frac{6}{5}a$. Find the value of $\bar{x}$. (Here, if $Z$ is a random variable following the standard normal distribution, $\mathrm{P}(|Z| \leq 1.96) = 0.95$.) [3 points]\\
(1) 15.2\\
(2) 15.4\\
(3) 15.6\\
(4) 15.8\\
(5) 16.0