(1) solve the corresponding problem for \(Z\) with the same value of \(c\), thereby obtaining the \(z\)-score, \(z^\ast\), of \(x^\ast\).For a normal random variable \(X\) with mean \(\mu\) and standard deviation \(\sigma\), the problem of finding the number \(x^\ast\) so that \(P(Xx^\ast )\) is a specified value \(c\)) is solved in two steps:.The problem of finding the number \(z^\ast\) so that the probability \(P(Zz^\ast )\) is a specified value \(c\) is solved by looking for the complementary probability \(1-c\) in the interior of Figure 5.3.1 and reading \(z^\ast\) from the margins.\): Distribution of Times to Run a CourseĪ boy has an average finishing time if he runs the course with a time between \(26.7\) and \(31.3\) minutes, or equivalently between \(26\) minutes \(42\) seconds and \(31\) minutes \(18\) seconds.
