3 A population has mean 12 and standard deviation 2.5. A large random sample of size \(n\) is chosen from this population and the sample mean is denoted by \(\bar { X }\). Given that \(\mathrm { P } ( \bar { X } < 12.2 ) = 0.975\), correct to 3 significant figures, find the value of \(n\).

3 A population has mean 12 and standard deviation 2.5. A large random sample of size $n$ is chosen from this population and the sample mean is denoted by $\bar { X }$. Given that $\mathrm { P } ( \bar { X } < 12.2 ) = 0.975$, correct to 3 significant figures, find the value of $n$.\\

\hfill \mbox{\textit{CAIE S2 2018 Q3}}