Moderate -0.3 This is a standard two-equation system for finding normal distribution parameters. The first probability immediately gives μ = 54.1 (since P(X < μ) = 0.5), then the second probability requires a single z-score lookup and simple algebra to find σ. Straightforward application of normal distribution properties with minimal calculation steps.
2 The random variable \(X\) has the distribution \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\). It is given that \(\mathrm { P } ( X < 54.1 ) = 0.5\) and \(\mathrm { P } ( X > 50.9 ) = 0.8665\). Find the values of \(\mu\) and \(\sigma\).
2 The random variable $X$ has the distribution $\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)$. It is given that $\mathrm { P } ( X < 54.1 ) = 0.5$ and $\mathrm { P } ( X > 50.9 ) = 0.8665$. Find the values of $\mu$ and $\sigma$.
\hfill \mbox{\textit{CAIE S1 2015 Q2 [4]}}