Question

Given the shaded area under the standard normal curve to be 0.04, find the following:

(a) left-tailed z value

z=

(b) right-tailed z value

z=

(c) two-tailed z value (note you are only being asked to report the positive z value)

|z|=

Answer 1

a)

We have to calculate z such that

P( Z < z) = 0.04

From the Z table, z-score for the probability of 0.04 is -1.75

z = -1.75

b)

We have to calculate z such that

P( Z > z) = 0.04

That is

P( Z < z) = 0.96

From Z table, z-score for the probability of 0.96 is 1.75

z = 1.75

We have to calulate z such that

P( |Z| < z) = 0.04

That is

P( -z < Z < z) = 0.04

P( Z < z) - P( Z < -z) = 0.04

P( Z < z) - ( 1 - P( Z < z) ) = 0.04

P( Z < z) - 1 + P( Z < z) = 0.04

2 P( Z < z) = 1.04

P( Z < z) = 0.52

From the Z table, z-score for the probability of 0.52 is 0.05

Therefore,

|z| = 0.05