Standard Normal Random Variable Only Answer A C E For a stan

Standard Normal Random Variable (Only Answer A, C, E)

For a standard normal random variable Z, find a number z_0 such that the following probabilities are obtained. P(Z LE z_0)=0.1 P(Z LE z_0)=0.78 P(Z GE z_0)=0.05 P(Z GE z_0)=0.82 P(-z_0 LE Z LE z_0)=0.95 P(|Z| GE z_0)=0.50

Solution

a. P(Z <=Z0) = 0.1

Z₀ = -1.282

c. P(Z > Z₀) = 0.05

Z₀ = 1.645

e. P( |Z| > Z₀ ) = 0.50

or, P(Z < -Z₀ ) + P(Z> Z₀ ) = 0.50

or, P(Z < -Z₀ ) = 0.25

Z₀ = 0.674