Mean of the normal distribution is \mu = 80 and the standard deviation is \(\displaystyle\sigma={14}\)

Let X be the random variable.

\(\displaystyle{P}{\left({X}{<}{75}\right)}={P}{\left({X}-\mu{<}{75}-\mu\right)}\)

\(\displaystyle={P}{\left({\frac{{{X}-\mu}}{{\sigma}}}{<}{\frac{{{75}-\mu}}{{\sigma}}}\right)}\)

\(\displaystyle={P}{\left({z}{<}{\frac{{{75}-{80}}}{{{14}}}}\right)}\)

\(\displaystyle={P}{\left({z}{<}{\frac{{-{5}}}{{{14}}}}\right)}\)

=P(z<-0.357)

=P(z>0.357)

=0.5-P(0 =0.5-0.14-6 (from Appendix B1.)

=0.3594