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Chapter 6: Q. 6.82 (page 269)

Determine the two z-scores that divide the area under the standard normal curve into a middle 0.99area and two outside0.005 areas.

Short Answer

Expert verified

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

The z-score with the area 0.005to its right under the conventional normal curve will be2.575.

Step by step solution

01

Given information

The given areas are

Middle area is 0.99

Two outside areas are0.005.

02

Explanation

The given middle area is 0.99.

The two outside areas are 0.005

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

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

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

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

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