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Chapter 6: Problem 44

In a standard Normal distribution, if the area to the left of a \(z\) -score is about \(0.1000\), what is the approximate \(z\) -score?

Short Answer

Expert verified
The approximate z-score for an area of \(0.1000\) to its left in the standard Normal distribution is \(-1.28\).

Step by step solution

01

Understanding the Problem

We are asked to find the z-score which leaves an area of 0.1000 to its left in the standard Normal distribution. Area under the curve is also known as cumulative probability. In this case, the cumulative probability is given and we need to find the corresponding z-score.
02

Using the Z table or Calculator

A Z table or a calculator with a Z-distribution function allows us to find the z-score associated with a given area to the left of the score. For an area of \(0.1000\) to the left of the z-score, we look up \(0.1000\) in the body of the Z table or use the calculator function to find the corresponding z-score.
03

Finding the Z-Score

The z-score associated with a left-tail area of \(0.1000\) is about \(-1.28\). This means that approximately \(10\%\) of all data values are less (to the left) than this z-score in a standard Normal distribution.

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