Q. 6.81 - Elementary Statistics

Question

Determine the two $z-$scores that divide the area under the standard normal curve into a middle $0.90$ area and two outside $0.05$ areas.

Step-by-Step Solution

Answer

The $z-$score under the typical normal curve with area $0.05$ to the left is around $-1.645$. The $z-$score with the area $0.05$ to its right under the typical normal curve will be $1.645.$

Step 1: Given information

The given areas

Middle area is $0.90$

Two outside areas are $0.05.$

Step 2: Explanation

The given middle area is $0.90$

Two outside areas are $0.05.$

Begin by looking for the area $0.05$ in the table's body. It is not in the table, and the closest values are $0.0495$ and $0.0505$ in the table. $-1.645$ is the average of two $z-$scores of $-1.64$ and $-1.65$.

As a result, the $z-$score under the typical normal curve with area $0.05$ to the left is around $-1.645$. The $z-$score with the area $0.05$ to its right under the typical normal curve will be $1.645$ using the symmetry property, which can be depicted as

Below is a section of the standard normal table that is relevant: