Question

# Assume that the random variable Z follows standard normal distribution, calculate the following probabilities (Round to two decimal places)a)P(z>1.9)b)P(−2<=z<=1.2)c)P(z>−0.2)

Normal distributions

Assume that the random variable Z follows standard normal distribution, calculate the following probabilities (Round to two decimal places)
a)$$P(z>1.9)$$
b)$$\displaystyle{P}{\left(−{2}\le{z}\le{1.2}\right)}$$
c)$$P(z\geq0.2)$$

2020-11-06

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)$$P(z\geq0.2)=1-P(z\leq-0.2)$$
$$P(z\geq0.2) = 1−0.4207$$
$$\displaystyle{P}{\left({z}\geq{0.2}\right)}={0.5793}\approx{0.58}$$