Solutions - 5180-08

(1) Write $X=\sigma Z+\mu$ and substitute into the probability:

$$\begin{array}{c}X=40Z+60\\ \\ P[110<X<140]\gg \gg P[110<40Z+60<140]\\ \\ \gg \gg P[\frac{110-60}{40}<Z<\frac{140-60}{40}]\gg \gg P[1.25<Z<2]\end{array}$$

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(2) Evaluate using the $\mathrm{\Phi }$ table:

$$\begin{array}{c}\mathrm{\Phi }(2)-\mathrm{\Phi }(1.25)\gg \gg 0.97725-0.8944\gg \gg 0.08285\end{array}$$