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)

Question
Normal distributions
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>−0.2)

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)\(\displaystyle{P}{\left(−{2}\le{z}\le{1.2}\right)}={P}{\left({z}\le{1.2}\right)}−{P}{\left({z}{<}−{2}\right)}\)</span>
\(\displaystyle{P}{\left(−{2}\le{z}\le{1.2}\right)}={0.8849}−{0.0228}\)
\(\displaystyle{P}{\left(−{2}\le{z}\le{1.2}\right)}={0.8621}\approx{0.86}\)
c)\(\displaystyle{P}{\left({z}{>}−{0.2}\right)}={1}−{P}{\left({z}\le−{0.2}\right)}\)
P(z>−0.2) = 1−0.4207
\(\displaystyle{P}{\left({z}{>}−{0.2}\right)}={0.5793}\approx{0.58}\)
0

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