csat-suneung 2013 Q13

csat-suneung · South-Korea · csat__math-science 3 marks Normal Distribution Algebraic Relationship Between Normal Parameters and Probability
A random variable $X$ follows a normal distribution $\mathrm { N } \left( m , \sigma ^ { 2 } \right)$ and satisfies the following conditions.
(a) $\mathrm { P } ( X \geq 64 ) = \mathrm { P } ( X \leq 56 )$
(b) $\mathrm { E } \left( X ^ { 2 } \right) = 3616$ What is the value of $\mathrm { P } ( X \leq 68 )$ obtained using the table on the right? [3 points]
(1) 0.9104
(2) 0.9332
(3) 0.9544
(4) 0.9772
(5) 0.9938
$x$$\mathrm { P } ( m \leq X \leq x )$
$m + 1.5 \sigma$0.4332
$m + 2 \sigma$0.4772
$m + 2.5 \sigma$0.4938
A random variable $X$ follows a normal distribution $\mathrm { N } \left( m , \sigma ^ { 2 } \right)$ and satisfies the following conditions.\\
(a) $\mathrm { P } ( X \geq 64 ) = \mathrm { P } ( X \leq 56 )$\\
(b) $\mathrm { E } \left( X ^ { 2 } \right) = 3616$\\
What is the value of $\mathrm { P } ( X \leq 68 )$ obtained using the table on the right? [3 points]\\
(1) 0.9104\\
(2) 0.9332\\
(3) 0.9544\\
(4) 0.9772\\
(5) 0.9938

\begin{center}
\begin{tabular}{ | c | c | }
\hline
$x$ & $\mathrm { P } ( m \leq X \leq x )$ \\
\hline
$m + 1.5 \sigma$ & 0.4332 \\
\hline
$m + 2 \sigma$ & 0.4772 \\
\hline
$m + 2.5 \sigma$ & 0.4938 \\
\hline
\end{tabular}
\end{center}