csat-suneung 2012 Q16

csat-suneung · South-Korea · csat__math-humanities 4 marks Normal Distribution Sampling Distribution of the Mean
The length $X$ of products manufactured at a certain factory follows a normal distribution with mean $m$ and standard deviation 4. When $\mathrm { P } ( m \leq X \leq a ) = 0.3413$, what is the probability that the sample mean of the lengths of 16 products randomly selected from this factory is at least $a - 2$, using the standard normal distribution table on the right? (where $a$ is a constant and the unit of length is cm) [4 points]
$z$$\mathrm { P } ( 0 \leq Z \leq z )$
1.00.3413
1.50.4332
2.00.4772

(1) 0.0228
(2) 0.0668
(3) 0.0919
(4) 0.1359
(5) 0.1587 
The length $X$ of products manufactured at a certain factory follows a normal distribution with mean $m$ and standard deviation 4.\\
When $\mathrm { P } ( m \leq X \leq a ) = 0.3413$, what is the probability that the sample mean of the lengths of 16 products randomly selected from this factory is at least $a - 2$, using the standard normal distribution table on the right? (where $a$ is a constant and the unit of length is cm) [4 points]

\begin{center}
\begin{tabular}{ | c | c | }
\hline
$z$ & $\mathrm { P } ( 0 \leq Z \leq z )$ \\
\hline
1.0 & 0.3413 \\
\hline
1.5 & 0.4332 \\
\hline
2.0 & 0.4772 \\
\hline
\end{tabular}
\end{center}

(1) 0.0228\\
(2) 0.0668\\
(3) 0.0919\\
(4) 0.1359\\
(5) 0.1587
Paper Questions
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