The lifespan of monitors produced by a certain company follows a normal distribution. From a random sample of 100 monitors produced by this company, the sample mean is $\bar{x}$ and the sample standard deviation is 500. Using this result, the confidence interval for the mean lifespan of monitors produced by this company at a confidence level of $95\%$ is $[\bar{x} - c, \bar{x} + c]$. Find the value of $c$. (Here, $Z$ is a random variable following the standard normal distribution, and $\mathrm{P}(0 \leq Z \leq 1.96) = 0.4750$.) [3 points]
The lifespan of monitors produced by a certain company follows a normal distribution. From a random sample of 100 monitors produced by this company, the sample mean is $\bar{x}$ and the sample standard deviation is 500. Using this result, the confidence interval for the mean lifespan of monitors produced by this company at a confidence level of $95\%$ is $[\bar{x} - c, \bar{x} + c]$. Find the value of $c$. (Here, $Z$ is a random variable following the standard normal distribution, and $\mathrm{P}(0 \leq Z \leq 1.96) = 0.4750$.) [3 points]