In: Math
For a standard normal curve, find the z scores for the following: the lower and upper z-scores for the middle .7994
Solution:
we have to find two z scores for middle area = 0.7994
That is we have to find:
P( -z < Z < z) = 0.7994
Since area between -z to +z is 0.7994
then area left of -z and right of +z = 1 - 0.7994 = 0.2006
Thus area below -z is = 0.2006 / 2 = 0.1003
and area above +z is = 0.2006 /2 = 0.1003
Thus we get :
P( Z < -z) = 0.1003
Now look in z table for Area = 0.1003 or its closest area and find z value.
Area 0.1003 corresponds to -1.2 and 0.08 , that is: z = -1.28
That is: P( Z < -1.28) = 0.1003
Thus lower z value = -1.28
Now for upper z value:
Total area below z would be = P( Z < -z) + P( -z < Z < z)
P( Z < z) = 0.1003 + 0.7994
P( Z < z) = 0.8997
Look in z table for Area = 0.8997 and find corresponding z value.
Area 0.8997 corresponds to 1.2 and 0.08 , that is z = 1.28
That is :P( Z < 1.28) = 0.8997
Thus upper z value = 1.28
Thus we get Lower z = -1.28 and Upper z = 1.28