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
ANSWERED
asked 2020-11-05

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)\(P(z\geq0.2)\)

Expert Answers (1)

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

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