csat-suneung 2017 Q18

csat-suneung · South-Korea · csat__math-science 4 marks Normal Distribution Finding Unknown Mean from a Given Probability Condition
The random variable $X$ follows a normal distribution with mean $m$ and standard deviation 5, and the probability density function $f ( x )$ of the random variable $X$ satisfies the following conditions.
(a) $f ( 10 ) > f ( 20 )$
(b) $f ( 4 ) < f ( 22 )$ When $m$ is a natural number, what is the value of $\mathrm { P } ( 17 \leq X \leq 18 )$ obtained using the standard normal distribution table on the right? [4 points]
$z$$\mathrm { P } ( 0 \leq Z \leq z )$
0.60.226
0.80.288
1.00.341
1.20.385
1.40.419

(1) 0.044
(2) 0.053
(3) 0.062
(4) 0.078
(5) 0.097 
The random variable $X$ follows a normal distribution with mean $m$ and standard deviation 5, and the probability density function $f ( x )$ of the random variable $X$ satisfies the following conditions.\\
(a) $f ( 10 ) > f ( 20 )$\\
(b) $f ( 4 ) < f ( 22 )$\\
When $m$ is a natural number, what is the value of $\mathrm { P } ( 17 \leq X \leq 18 )$ obtained using the standard normal distribution table on the right? [4 points]
\begin{center}
\begin{tabular}{ | c | c | }
\hline
$z$ & $\mathrm { P } ( 0 \leq Z \leq z )$ \\
\hline
0.6 & 0.226 \\
\hline
0.8 & 0.288 \\
\hline
1.0 & 0.341 \\
\hline
1.2 & 0.385 \\
\hline
1.4 & 0.419 \\
\hline
\end{tabular}
\end{center}
(1) 0.044\\
(2) 0.053\\
(3) 0.062\\
(4) 0.078\\
(5) 0.097
Paper Questions
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