Find the value of ${ } ^ { z } \alpha / 2$ that corresponds to a confidence level of 89.48%.
A) 1.25
B) 1.62
C) -1.62
D) 0.0526

Question

Quizplus · Accepted Answer

To find the value of ${ } ^{z}\alpha / 2$ for a confidence level of 89.48%, we can use a standard normal distribution table or calculator to find the z-score that corresponds to the area to the right of the z-score being 0.0556 (since 1 - 0.8948 = 0.1052, and we want the area to the left to be 0.0556).

Using a standard normal distribution table or calculator, we can find that the z-score that corresponds to an area of 0.0556 to the right is approximately 1.62. Since we are looking for ${ }^{z}\alpha / 2$, we need to find the value of alpha that corresponds to a total area of 0.1052 (twice the area to the right of the z-score).

Using a standard normal distribution table or calculator, we can find that the z-score that corresponds to an area of 0.0526 to the right (half of 0.1052) is approximately 1.44. Thus, ${ }^{z}\alpha / 2$ is approximately 1.44, or -1.44 (since the standard normal distribution is symmetric about 0).

Since none of the answer choices are exactly 1.44 or -1.44, we can choose the best answer choice by selecting the one that is closest. In this case, B (1.62) is the closest, so the answer is B.

Find the Value Of zα/2{ } ^ { z } \alpha / 2zα/2

Find the Value Of ${ } ^ { z } \alpha / 2$