csat-suneung 2019 Q12

csat-suneung · South-Korea · csat__math-humanities 3 marks Confidence intervals Find a specific bound or margin of error from the CI formula
The weight of watermelons harvested in a certain village follows a normal distribution with mean $m$ kg and standard deviation 1.4 kg. When 49 watermelons are randomly sampled from this village and a 95\% confidence interval for the mean weight $m$ is constructed using the sample mean, the interval is $a \leq m \leq 7.992$. What is the value of $a$? (Here, when $Z$ is a random variable following the standard normal distribution, calculate using $\mathrm { P } ( | Z | \leq 1.96 ) = 0.95$.) [3 points]
(1) 7.198
(2) 7.208
(3) 7.218
(4) 7.228
(5) 7.238
The weight of watermelons harvested in a certain village follows a normal distribution with mean $m$ kg and standard deviation 1.4 kg. When 49 watermelons are randomly sampled from this village and a 95\% confidence interval for the mean weight $m$ is constructed using the sample mean, the interval is $a \leq m \leq 7.992$. What is the value of $a$? (Here, when $Z$ is a random variable following the standard normal distribution, calculate using $\mathrm { P } ( | Z | \leq 1.96 ) = 0.95$.) [3 points]\\
(1) 7.198\\
(2) 7.208\\
(3) 7.218\\
(4) 7.228\\
(5) 7.238