csat-suneung 2025 Q25

csat-suneung · South-Korea · csat__math 3 marks Confidence intervals Count integers or determine length of a confidence interval
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
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