Solutions - 5180-07

(a)

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

$$\begin{array}{c}X=4Z+14\\ \\ P[X>15]\gg \gg P[4Z+14>15]\\ \\ \gg \gg P[Z>\frac{15-14}{4}]\gg \gg P[Z>0.25]\end{array}$$

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

$$\begin{array}{c}\gg \gg 1-P[Z<0.25]\\ \\ \gg \gg 1-0.5987\gg \gg 0.4013\end{array}$$

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(b)

(1) Substitute $X=4Z+14$ into the probability:

$$P[X<10]\gg \gg P[4Z+14<10]\gg \gg P[Z<-1]$$

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

$$\begin{array}{c}1-P[Z<1]\gg \gg 1-0.8413\gg \gg 0.1587\end{array}$$