Question

Find the indicated probabilities using a standard normal distribution
a. P(Z < 1.85)
b. P(Z < -1.54 or Z > 1.54)

Answer 1

a) P( z < 1.85)

P( z < 1.85) = 0.9678

b. P(Z < -1.54 or Z > 1.54)

From table P(z < 1.54 ) = 0.9382

First we have to find P( z > 1.54 ) = 1 - P( z < 1.54) = 1 - 0.9382

Therefore P( z > 1.54 ) = 0.0618

Normal distribution is symmetric , therefore P( z > 1.54 ) = P( z < -1.54) = 0.0618

Therefore b. P(Z < -1.54 or Z > 1.54) = P( z > 1.54 ) + P( z < -1.54) = 0.0618 +0.018

P(Z < -1.54 or Z > 1.54) = 0.1236