Question

Find the critical value ( z_alpha/2 ) that corresponds to ( alpha = 0.19 ).

(A) ( z_0.095 )
(B) ( z_0.19 )
(C) ( z_0.905 )
(D) ( z_0.81 )

Answer 1

You need to find the critical value z_0.095 for α = 0.19 in a standard normal distribution, which approximately corresponds to z = 1.645.

Step-by-step explanation:

The question asks to find the critical value zα/2 corresponding to α = 0.19. This critical value marks the borderline in the tail of a standard normal distribution. Because we have a two-tailed test, the area in each tail is α/2 = 0.19/2 = 0.095. To find the value z0.095 using a standard normal probability table or calculator, we look up the z-score that has 0.905 (1-0.095) of the area to its left. The closest value in the typical z-tables to 0.905 will give us our critical z-value, which is approximately z = 1.645.