Step 1:

$X\sim N(80,10^2)$

Let $Z=\large\frac{X-\mu}{\sigma}$

The probability density function $Z$ is $\phi(z)=\large\frac{1}{\sqrt{2\pi}}$$e^{-\Large\frac{1}{2}z^2};-\infty < Z < \infty$

Step 2:

$P(70 < X)$

When $X=70$

$Z=\large\frac{70-80}{10}$$=-1$

$P(70 < X)=P(-1 < Z)$

$\qquad\qquad=P(0 < Z < 1)+0.5$

$\qquad\qquad=0.3413+0.5$

$\qquad\qquad=0.8413$