The weight of pomegranates produced at a certain farm follows a normal distribution with mean $m$ and standard deviation 40. A sample of size 64 was taken from the pomegranates produced at this farm, and the sample mean of the pomegranate weights was $\bar { x }$. Using this result, the 99\% confidence interval for the mean $m$ of the pomegranate weights produced at this farm is $\bar { x } - c \leq m \leq \bar { x } + c$. What is the value of $c$? (Here, the unit of weight is g, and when $Z$ is a random variable following the standard normal distribution, $\mathrm { P } ( 0 \leq Z \leq 2.58 ) = 0.495$.) [4 points] (1) 25.8 (2) 21.5 (3) 17.2 (4) 12.9 (5) 8.6
The weight of pomegranates produced at a certain farm follows a normal distribution with mean $m$ and standard deviation 40. A sample of size 64 was taken from the pomegranates produced at this farm, and the sample mean of the pomegranate weights was $\bar { x }$. Using this result, the 99\% confidence interval for the mean $m$ of the pomegranate weights produced at this farm is $\bar { x } - c \leq m \leq \bar { x } + c$. What is the value of $c$? (Here, the unit of weight is g, and when $Z$ is a random variable following the standard normal distribution, $\mathrm { P } ( 0 \leq Z \leq 2.58 ) = 0.495$.) [4 points]\\
(1) 25.8\\
(2) 21.5\\
(3) 17.2\\
(4) 12.9\\
(5) 8.6