Exercise 119 7 points Finding an unknown valueUse Table B or

Exercise 11.9 (7 points) Finding an unknown value.Use Table B or software to find the value z of a standard normal variable that satisfies each of the following conditions. (If using Table B, select the value of z in the table 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 25% of the observations falling below it.

b)The point z with 40% of the observations falling above it.

Solution

a)
P ( Z < x ) = 0.25
Value of z to the cumulative probability of 0.25 from normal table is -0.674
P( x-u/s.d < x - 0/1 ) = 0.25
That is, ( x - 0/1 ) = -0.67
--> x = -0.67 * 1 + 0 = -0.674                  
b)
P ( Z > x ) = 0.6
Value of z to the cumulative probability of 0.6 from normal table is -0.25
P( x-u/ (s.d) > x - 0/1) = 0.6
That is, ( x - 0/1) = -0.25
--> x = -0.25 * 1+0 = -0.253