Question

Find the following z values for the standard normal variable Z. (You may find it useful to reference the z table. Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

	a. P(Z ≤ z) = 0.1002 b. P(z ≤ Z ≤ 0) = 0.121 c. P(Z > z ) = 0.8204 d. P(0.36 ≤ Z ≤ z) = 0.3458

explain

Answer 1

Solution:

Given that,

a ) P( Z z ) = 0.1002

Using standard normal table

z = - 1.2804

b )   P(z Z   0 ) = 0.121

P ( Z   0 ) - P ( Z   z  ) = 0.121

Using standard normal table

P ( Z   z  ) = 0.5000 +  0.121

P ( Z   z  ) = 0.621

z = 0.3081

c )  P ( Z >  z  ) = 0.8204

= 1 - P ( Z < z  ) = 0.8204

Using standard normal table

P ( Z < z  ) = 1 -  0.8204

P ( Z < z  ) = 0.1796

z = - 0.91689

d )   P( 0.36 Z   z ) = 0.3458

P ( Z   z ) - P ( Z   0.36 ) = 0.3458

Using standard normal table

P ( Z   z  ) = 0.6406 + 0.3458

P ( Z   z  ) = 0.9864

z = 2.2086