Question

Answer the following questions. (a) State the z-score that has an area of 0.0885 on its right side. (b) State the z-score that has an area of 0.9804 on its left side. (c) State the z-score that has an area of 0.0164 on its right side. (d) State the z-score that has an area of 0.3246 on its left side.

Answer 1

a) We want to find, the z-score such that, P(Z > z) = 0.0885

P(Z > z) = 0.0885

=> 1 - P(Z < z) = 0.0885

=> P(Z < z) = 0.9115

Using standard normal z-table we get, z-score corresponds to probability 0.9115 is, z = 1.35

=> P(Z > 1.35) = 0.0885

Therefore, z-score = 1.35

b) We want to find, the z-score such that, P(Z < z) = 0.9804

P(Z < z) = 0.9804

Using standard normal z-table we get, z-score corresponds to probability 0.9804 is, z = 2.06

=> P(Z < 2.06) = 0.9804

Therefore, z-score = 2.06

c) We want to find, the z-score such that, P(Z > z) = 0.0164

P(Z > z) = 0.0164

=> 1 - P(Z < z) = 0.0164

=> P(Z < z) = 0.9836

Using standard normal z-table we get, z-score corresponds to probability 0.9836 is, z = 2.13

=> P(Z > 2.13) = 0.0164

Therefore, z-score = 2.13

d) We want to find, the z-score such that, P(Z < z) = 0.3246

P(Z < z) = 0.3246

Using standard normal z-table we get, z-score corresponds to probability 0.3246 is, z = -0.45487

=> P(Z < -0.45) = 0.3246

Therefore, z-score = - 0.455