Standard +0.3 This is a straightforward application of the central limit theorem requiring students to recognize that the sample mean has distribution N(23.0, 5.0²/n), then use the given probability to find n by standardizing and using inverse normal tables. It's slightly above average difficulty because it requires working backwards from a probability to find n, but the setup is clear and the method is standard for S2.
2 The continuous random variable \(Y\) has the distribution \(\mathrm { N } \left( 23.0,5.0 ^ { 2 } \right)\). The mean of \(n\) observations of \(Y\) is denoted by \(\bar { Y }\). It is given that \(\mathrm { P } ( \bar { Y } > 23.625 ) = 0.0228\). Find the value of \(n\).
2 The continuous random variable $Y$ has the distribution $\mathrm { N } \left( 23.0,5.0 ^ { 2 } \right)$. The mean of $n$ observations of $Y$ is denoted by $\bar { Y }$. It is given that $\mathrm { P } ( \bar { Y } > 23.625 ) = 0.0228$. Find the value of $n$.
\hfill \mbox{\textit{OCR S2 2009 Q2 [4]}}