Standard +0.3 This is a standard S2 question requiring students to set up two equations using inverse normal values (z = 1.645 and z = -0.674) and solve simultaneously for μ and σ. While it involves multiple steps, the method is routine and commonly practiced in S2 courses, making it slightly easier than average.
1 The random variable \(T\) is normally distributed with mean \(\mu\) and standard deviation \(\sigma\). It is given that \(\mathrm { P } ( T > 80 ) = 0.05\) and \(\mathrm { P } ( T > 50 ) = 0.75\). Find the values of \(\mu\) and \(\sigma\).
1 The random variable $T$ is normally distributed with mean $\mu$ and standard deviation $\sigma$. It is given that $\mathrm { P } ( T > 80 ) = 0.05$ and $\mathrm { P } ( T > 50 ) = 0.75$. Find the values of $\mu$ and $\sigma$.
\hfill \mbox{\textit{OCR S2 2008 Q1 [6]}}