Question

Find the value z of a standard Normal variable that satisfies each of the following conditions.

(a) The point z with 20% of the observations falling below it
z=

(b) The point z with 10% of the observations falling above it

z=

Answer 1

Solution:

We have to find  the value z of a standard Normal variable that satisfies each of the following conditions.

Part a) The point z with 20% of the observations falling below it

That is find z value such that:

P( Z < z )= 20%

P( Z < z )= 0.20

Thus look in z table for Area = 0.2000 or its closest area and find corresponding z value.

Area 0.2005 is closest to 0.2000 and it corresponds to -0.8 and 0.04

Thus z value = -0.84

Thus  20% of the observations falling below z = -0.84

Part b) The point z with 10% of the observations falling above it

That is find:

P( Z > z ) = 0.10

Thus we get:

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

P( Z< z ) = 1 - 0.10

P( Z< z ) = 0.90

Thus look in z table for area = 0.9000 or its closest area and find z value:

Area 0.8997 is closest to 0.9000 and it corresponds to 1.2 and 0.08

thus z = 1.28

Thus 10% of the observations falling above z = 1.28