Question

Complete the following table.

Short answer

The completed table is given below,

$z_{0.10}$	$z_{0.05}$	$z_{0.025}$	$z_{0.01}$	$z_{0.005}$
$1.28$	$1.645$	$1.96$	$2.33$	$2.575$

Step-by-step solution

Step 1. Given information

Step 2. Find the value for z0.05.

The area $0.05$is not found in the table. So, we can use area closest to $0.05$which are $0.0495$and $0.0505$. Here, we use the average of the two $z$-scores $1.64$and $1.65$, which is $-1.645$. Thus, the $z$-score having area $0.05$to its left under the standard normal curve is$-1.645$. By applying the symmetry property the$z$-score having area$0.05$to its right under the standard normal curve is,$1.645$.

Step 3. Find the value for z0.025.

The value of $z$-score for the area $0.025$in the table is,$-1.96$. Thus, the$z$-score having area$0.025$to its left under the standard normal curve is,$-1.96$. By applying the symmetry property the$z$-score having area$0.025$to its right under the standard normal curve is$1.96$.

Step 4. Find the value for z0.01.

The $z$-score for the area $0.01$is not found in the table. So, we use the area closest to $0.01$, which is $0.0099$. The $z$-score corresponding to that area is, $-2.33$. Thus, the $z$-score having area $0.01$to its left under the standard normal curve is, $-2.33$. By applying the symmetry property the $z$-score having area$0.01$to its right under the standard normal curve is,$2.33$.

Step 5. Find the value for z0.005.

The area $0.005$has no value in the table. So, we use area closest to $0.005$, which are $0.0049$and $0.0051$. Here, we use the average of the two $z$-scores $-2.57$and $-2.58$, which is $-2.575$. Thus, the $z$-score having area $0.005$to its left under the standard normal curve is, $-2.575$. By applying the symmetry property the $z$-score having area $0.005$to its right under the standard normal curve is, $2.575$.