Find the critical value $z_{c}$ necessary to form a confidence interval at the level of confidence shown below.
\[
c=0.94
\]
\[
\mathrm{z}_{\mathrm{c}}=
\]
(Round to two decimal places as needed.)
Answer
Rounding to two decimal places, the critical value $z_c$ necessary to form a confidence interval at the level of confidence $c=0.94$ is approximately \(\boxed{1.88}\).
Step 1 ：The critical value $z_c$ is the z-score such that the area under the standard normal curve between $-z_c$ and $z_c$ is equal to the confidence level $c$.
Step 2 ：Since the standard normal curve is symmetric, the area in each tail is $(1 - c) / 2$. Therefore, we need to find the z-score such that the area to the left of it is $1 - (1 - c) / 2 = (c + 1) / 2$.
Step 3 ：Given that the confidence level $c = 0.94$, we find that the critical value $z_c$ is approximately 1.8807936081512509.
Step 4 ：Rounding to two decimal places, the critical value $z_c$ necessary to form a confidence interval at the level of confidence $c=0.94$ is approximately \(\boxed{1.88}\).
