csat-suneung 2014 Q12

csat-suneung · South-Korea · csat__math-A 3 marks Linear combinations of normal random variables
A pharmaceutical company produces medicine bottles with capacity following a normal distribution with mean $m$ and standard deviation 10. When a random sample of 25 bottles is taken from the company's production, the probability that the sample mean capacity is at least 2000 is 0.9772. Using the standard normal distribution table below, what is the value of $m$? (Here, the unit of capacity is mL.) [3 points]
$z$$\mathrm { P } ( 0 \leq Z \leq z )$
1.50.4332
2.00.4772
2.50.4938
3.00.4987

(1) 2003
(2) 2004
(3) 2005
(4) 2006
(5) 2007 
A pharmaceutical company produces medicine bottles with capacity following a normal distribution with mean $m$ and standard deviation 10. When a random sample of 25 bottles is taken from the company's production, the probability that the sample mean capacity is at least 2000 is 0.9772. Using the standard normal distribution table below, what is the value of $m$? (Here, the unit of capacity is mL.) [3 points]

\begin{center}
\begin{tabular}{ | c | c | }
\hline
$z$ & $\mathrm { P } ( 0 \leq Z \leq z )$ \\
\hline
1.5 & 0.4332 \\
\hline
2.0 & 0.4772 \\
\hline
2.5 & 0.4938 \\
\hline
3.0 & 0.4987 \\
\hline
\end{tabular}
\end{center}

(1) 2003\\
(2) 2004\\
(3) 2005\\
(4) 2006\\
(5) 2007
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