Question

1. which confidence level corresponds to a z - score of 1.96?

a. 95%
b. 85%
c. 99%
d. 90%

Explanation:

Step1: Recall Z - score and confidence level relationship

In a standard normal distribution, for a two - tailed test, the area between $-z$ and $z$ gives the confidence level. A $z$-score of 1.96 means that the area in the two tails is $(1 - \text{confidence level})$. The area in each tail is $\frac{1 - \text{confidence level}}{2}$. For $z = 1.96$, the area in each tail is 0.025.

Step2: Calculate the confidence level

The total area in the two tails is $2\times0.025=0.05$. So the confidence level is $1 - 0.05=0.95$ or 95%.

Answer:

A. 95%