csat-suneung 2010 Q9

csat-suneung · South-Korea · csat__math-humanities 4 marks Normal Distribution Process Capability or Quality Compliance Assessment
The internal pressure strength of bottles produced at a certain factory follows a normal distribution $\mathrm { N } \left( m , \sigma ^ { 2 } \right)$, and bottles with internal pressure strength less than 40 are classified as defective. The process capability index $G$ for evaluating the factory's process capability is calculated as $$G = \frac { m - 40 } { 3 \sigma }$$ When $G = 0.8$, what is the probability that a randomly selected bottle is defective, using the standard normal distribution table on the right? [4 points]
$z$$\mathrm { P } ( 0 \leqq Z \leqq z )$
2.20.4861
2.30.4893
2.40.4918
2.50.4938

(1) 0.0139
(2) 0.0107
(3) 0.0082
(4) 0.0062
(5) 0.0038 
The internal pressure strength of bottles produced at a certain factory follows a normal distribution $\mathrm { N } \left( m , \sigma ^ { 2 } \right)$, and bottles with internal pressure strength less than 40 are classified as defective. The process capability index $G$ for evaluating the factory's process capability is calculated as
$$G = \frac { m - 40 } { 3 \sigma }$$
When $G = 0.8$, what is the probability that a randomly selected bottle is defective, using the standard normal distribution table on the right? [4 points]

\begin{center}
\begin{tabular}{ | c | c | }
\hline
$z$ & $\mathrm { P } ( 0 \leqq Z \leqq z )$ \\
\hline
2.2 & 0.4861 \\
2.3 & 0.4893 \\
2.4 & 0.4918 \\
2.5 & 0.4938 \\
\hline
\end{tabular}
\end{center}

(1) 0.0139\\
(2) 0.0107\\
(3) 0.0082\\
(4) 0.0062\\
(5) 0.0038
Paper Questions
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