Question

Find the following z values for the standard normal variable Z. (Use Excel command instead of the z table. Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

a.	P(Z ≤ z) = 0.9477
b.	P(Z > z) = 0.63
c.	P(−z ≤ Z ≤ z) = 0.85
d.	P(0 ≤ Z ≤ z) = 0.2034

Answer 1

Solution:

Part a

	a. P(Z ≤ z) = 0.9477

The value of the z by using excel command =NORMSINV(0.9477) is given as below:

z = 1.622950439

z = 1.62

Part b

b.	P(Z > z) = 0.63

The value of the z by using excel command =NORMSINV(1 - 0.63) is given as below:

z = -0.33185335

z = -0.33

Part c

c.	P(−z ≤ Z ≤ z) = 0.85

The value of the z by using excel command =-NORMSINV((1 - 0.85)/2) is given as below:

z = 1.43953147

z = 1.44

Part d

d.	P(0 ≤ Z ≤ z) = 0.2034

We know P(Z≤0) = 0.5

The value of the z by using excel command =NORMSINV(0.5+0.2034) is given as below:

z = 0.534204581

z = 0.53