find the value z of a standard Normal variable that satisfie

find the value z of a standard Normal variable that satisfies each of the following conditions. (Use the value of z from Table A that comes closest to satisfying the condition.) In each case, sketch a standard Normal curve with your value of z marked on the axis.

(a) The point z with 66% of the observations falling below it

z (±0.01) =

(b) The point z with 22% of the observations falling above it

z (±0.01) =

Solution

a)
P ( Z < x ) = 0.66
Value of z to the cumulative probability of 0.66 from normal table is 0.412
P( x-u/s.d < x - 0/1 ) = 0.66
That is, ( x - 0/1 ) = 0.41
--> x = 0.41 * 1 + 0 = 0.412                  
b)
P ( Z > x ) = 0.22
Value of z to the cumulative probability of 0.22 from normal table is 0.77
P( x-u/ (s.d) > x - 0/1) = 0.22
That is, ( x - 0/1) = 0.77
--> x = 0.77 * 1+0 = 0.772