Q. 6.8 - Elementary Statistics

Question

Complete the following table.

Step-by-Step Solution

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 1 . Given information

Step 2 . Find the value for z 0 . 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 z 0 . 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 z 0 . 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 z 0 . 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, $2.575$.