A certain automobile company produces electric vehicles whose driving range on a single charge follows a normal distribution with mean $m$ and standard deviation $\sigma$. When a sample of 100 electric vehicles produced by this company is randomly selected and the sample mean of the driving range is $\overline { x _ { 1 } }$, the 95\% confidence interval for the population mean $m$ is $a \leq m \leq b$. When a sample of 400 electric vehicles produced by this company is randomly selected and the sample mean of the driving range is $\overline { x _ { 2 } }$, the 99\% confidence interval for the population mean $m$ is $c \leq m \leq d$. If $\overline { x _ { 1 } } - \overline { x _ { 2 } } = 1.34$ and $a = c$, what is the value of $b - a$? (Here, the unit of driving range is km, and when $Z$ is a random variable following the standard normal distribution, $\mathrm { P } ( | Z | \leq 1.96 ) = 0.95 , \mathrm { P } ( | Z | \leq 2.58 ) = 0.99$.) [3 points] (1) 5.88 (2) 7.84 (3) 9.80 (4) 11.76 (5) 13.72
A certain automobile company produces electric vehicles whose driving range on a single charge follows a normal distribution with mean $m$ and standard deviation $\sigma$.
When a sample of 100 electric vehicles produced by this company is randomly selected and the sample mean of the driving range is $\overline { x _ { 1 } }$, the 95\% confidence interval for the population mean $m$ is $a \leq m \leq b$.
When a sample of 400 electric vehicles produced by this company is randomly selected and the sample mean of the driving range is $\overline { x _ { 2 } }$, the 99\% confidence interval for the population mean $m$ is $c \leq m \leq d$.
If $\overline { x _ { 1 } } - \overline { x _ { 2 } } = 1.34$ and $a = c$, what is the value of $b - a$? (Here, the unit of driving range is km, and when $Z$ is a random variable following the standard normal distribution, $\mathrm { P } ( | Z | \leq 1.96 ) = 0.95 , \mathrm { P } ( | Z | \leq 2.58 ) = 0.99$.) [3 points]\\
(1) 5.88\\
(2) 7.84\\
(3) 9.80\\
(4) 11.76\\
(5) 13.72