Given:

random variable z follows the standard normal distributions.

a)\(\displaystyle{P}{\left({z}{>}{1.9}\right)}={1}−{P}{\left({z}\le{1.9}\right)}\)

\(P(z>1.9) = 1−0.9713\)

\(\displaystyle{P}{\left({z}{>}{1.9}\right)}={0.0287}\approx{0.03}\)

b)\(P(-2\leq z\leq1.2)=P(z\leq1.2)-P(z\leq2)\)

\(\displaystyle{P}{\left(−{2}\le{z}\le{1.2}\right)}={0.8849}−{0.0228}\)

\(\displaystyle{P}{\left(−{2}\le{z}\le{1.2}\right)}={0.8621}\approx{0.86}\)

c)\(P(z\geq0.2)=1-P(z\leq-0.2)\)

\(P(z\geq0.2) = 1−0.4207\)

\(\displaystyle{P}{\left({z}\geq{0.2}\right)}={0.5793}\approx{0.58}\)