csat-suneung 2016 Q18

csat-suneung · South-Korea · csat__math-B 4 marks Normal Distribution Sampling Distribution of the Mean
From a population following a normal distribution $\mathrm { N } \left( 50,8 ^ { 2 } \right)$, a sample of size 16 is randomly extracted to obtain the sample mean $\bar { X }$. From a population following a normal distribution $\mathrm { N } \left( 75 , \sigma ^ { 2 } \right)$, a sample of size 25 is randomly extracted to obtain the sample mean $\bar { Y }$. When $\mathrm { P } ( \bar { X } \leq 53 ) + \mathrm { P } ( \bar { Y } \leq 69 ) = 1$, what is the value of $\mathrm { P } ( \bar { Y } \geq 71 )$ using the standard normal distribution table below?
$z$$\mathrm { P } ( 0 \leq Z \leq z )$
1.00.3413
1.20.3849
1.40.4192
1.60.4452

[4 points]
(1) 0.8413
(2) 0.8644
(3) 0.8849
(4) 0.9192
(5) 0.9452 
From a population following a normal distribution $\mathrm { N } \left( 50,8 ^ { 2 } \right)$, a sample of size 16 is randomly extracted to obtain the sample mean $\bar { X }$. From a population following a normal distribution $\mathrm { N } \left( 75 , \sigma ^ { 2 } \right)$, a sample of size 25 is randomly extracted to obtain the sample mean $\bar { Y }$.\\
When $\mathrm { P } ( \bar { X } \leq 53 ) + \mathrm { P } ( \bar { Y } \leq 69 ) = 1$, what is the value of $\mathrm { P } ( \bar { Y } \geq 71 )$ using the standard normal distribution table below?
\begin{center}
\begin{tabular}{ | c | c | }
\hline
$z$ & $\mathrm { P } ( 0 \leq Z \leq z )$ \\
\hline
1.0 & 0.3413 \\
\hline
1.2 & 0.3849 \\
\hline
1.4 & 0.4192 \\
\hline
1.6 & 0.4452 \\
\hline
\end{tabular}
\end{center}
[4 points]\\
(1) 0.8413\\
(2) 0.8644\\
(3) 0.8849\\
(4) 0.9192\\
(5) 0.9452
Paper Questions
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