Find the value of z subscript alpha divided by 2 (Z_α/2) that corresponds to a confidence level of 89.48%.

Solution:

Given, confidence level c = 89.48%

c in decimal = 89.48 / 100 = 0.8948

Significance level, 𝛼 = 1 - c

𝛼 = 1 - 0.8948

𝛼 = 0.1052

Now, we have to find the value of Z_{𝛼 /2}

𝛼 / 2 = 0.1052 / 2 = 0.0526

Now, find the z-value for 𝛼 / 2 = 0.0526

Using z table, 

Zα / 2 = ± 1.620

Therefore, the value of z subscript alpha divided by 2 is ± 1.620

Find the value of z subscript alpha divided by 2 (Z_α/2) that corresponds to a confidence level of 89.48%.

Summary:

The value of z subscript alpha divided by 2 (Z_α/2) that corresponds to a confidence level of 89.48% is ± 1.620.