A factory produces table tennis balls. When dropped from a certain height onto a steel floor, the height to which the table tennis ball bounces follows a normal distribution. From the table tennis balls produced by this factory, 100 balls were randomly sampled and the bounce height was measured, resulting in a mean of 245 and a standard deviation of 20.
What is the number of integers in the 95\% confidence interval for the mean bounce height of all table tennis balls produced by this factory? (Here, the unit of height is mm, and when $Z$ follows the standard normal distribution, $\mathrm { P } ( 0 \leqq Z \leqq 1.96 ) = 0.4750$.) [3 points]
(1) 5
(2) 6
(3) 7
(4) 8
(5) 9

For a normal distribution with known standard deviation $\sigma$, a sample of size $n$ is randomly extracted from the population. The 95\% confidence interval for the population mean obtained from this sample is [100.4, 139.6]. Using the same sample, find the number of natural numbers contained in the 99\% confidence interval for the population mean. (Given that when $Z$ is a random variable following the standard normal distribution, $\mathrm { P } ( 0 \leq Z \leq 1.96 ) = 0.475$ and $\mathrm { P } ( 0 \leq Z \leq 2.58 ) = 0.495$.) [3 points]

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