csat-suneung 2012 Q9

csat-suneung · South-Korea · csat__math-science 3 marks Confidence intervals Algebraic problem using two confidence intervals
The calcium content in one bottle of beverage produced by a certain company follows a normal distribution with population mean $m$ and population standard deviation $\sigma$. When 16 bottles of beverage produced by this company were randomly sampled and the calcium content was measured, the sample mean was 12.34. When the 95\% confidence interval for the population mean $m$ of the calcium content in one bottle of beverage produced by this company is $11.36 \leq m \leq a$, what is the value of $a + \sigma$? (Note: When $Z$ follows the standard normal distribution, $\mathrm { P } ( 0 \leq Z \leq 1.96 ) = 0.4750$, and the unit of calcium content is mg.) [3 points]
(1) 14.32
(2) 14.82
(3) 15.32
(4) 15.82
(5) 16.32
The calcium content in one bottle of beverage produced by a certain company follows a normal distribution with population mean $m$ and population standard deviation $\sigma$. When 16 bottles of beverage produced by this company were randomly sampled and the calcium content was measured, the sample mean was 12.34. When the 95\% confidence interval for the population mean $m$ of the calcium content in one bottle of beverage produced by this company is $11.36 \leq m \leq a$, what is the value of $a + \sigma$? (Note: When $Z$ follows the standard normal distribution, $\mathrm { P } ( 0 \leq Z \leq 1.96 ) = 0.4750$, and the unit of calcium content is mg.) [3 points]\\
(1) 14.32\\
(2) 14.82\\
(3) 15.32\\
(4) 15.82\\
(5) 16.32