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]
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]