A sample of size 256 is randomly extracted from a population following a normal distribution $\mathrm{N}\left(m, 2^{2}\right)$. The 95\% confidence interval for $m$ obtained using the sample mean is $a \leq m \leq b$. What is the value of $b - a$? (Given: When $Z$ is a random variable following the standard normal distribution, $\mathrm{P}(|Z| \leq 1.96) = 0.95$.) [3 points]
(1) 0.49
(2) 0.52
(3) 0.55
(4) 0.58
(5) 0.61

A population with mean $m$ and standard deviation 5 follows a normal distribution. A sample of size 36 is randomly extracted, and the 99\% confidence interval for the population mean $m$ obtained using the sample mean is $1.2 \leq m \leq a$. What is the value of $a$? (When $Z$ is a random variable following the standard normal distribution, calculate using $\mathrm { P } ( | Z | \leq 2.58 ) = 0.99$.) [3 points]
(1) 5.1
(2) 5.2
(3) 5.3
(4) 5.4
(5) 5.5