Q. 6.82 - Elementary Statistics

Question

Determine the two $z-$scores that divide the area under the standard normal curve into a middle $0.99$ area and two outside $0.005$ areas.

Step-by-Step Solution

Answer

The $z-$score under the usual normal curve with area $0.005$ to the left is around $-2.575$.

The $z-$score with the area $0.005$ to its right under the conventional normal curve will be $2.575.$

Step 1: Given information

The given areas are

Middle area is $0.99$

Two outside areas are $0.005.$

Step 2: Explanation

The given middle area is $0.99.$

The two outside areas are $0.005$

Begin by looking for the $0.005$ area in the table's body. It is not included in the table, and the closest values are $0.0049$ and $0.0051$. $-2.575$ is the average of two $z-$scores of $-2.57$ and $-2.58$.

As a result, the z-score under the usual normal curve with area $0.005$ to the left is around $-2.575.$

The z-score with the area $0.005$ to its right under the conventional normal curve will be $2.575$ using the symmetry property, which can be depicted as

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