Standard +0.3 This is a standard S2 inverse normal problem requiring students to set up two equations using z-scores from given probabilities, then solve simultaneously for μ and σ. While it involves multiple steps (looking up inverse normal values, forming equations, solving), it's a routine textbook exercise with no novel insight required—slightly above average difficulty due to the algebraic manipulation needed.
1 The random variable \(H\) has the distribution \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\). It is given that \(\mathrm { P } ( H < 105.0 ) = 0.2420\) and \(\mathrm { P } ( H > 110.0 ) = 0.6915\). Find the values of \(\mu\) and \(\sigma\), giving your answers to a suitable degree of accuracy.
1 The random variable $H$ has the distribution $\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)$. It is given that $\mathrm { P } ( H < 105.0 ) = 0.2420$ and $\mathrm { P } ( H > 110.0 ) = 0.6915$. Find the values of $\mu$ and $\sigma$, giving your answers to a suitable degree of accuracy.
\hfill \mbox{\textit{OCR S2 2009 Q1 [6]}}