Questions: Use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area 0.0038. z= (Type an integer or decimal rounded to two decimal places as needed.)

Use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area 0.0038.
z= (Type an integer or decimal rounded to two decimal places as needed.)

Transcript text: Use the Standard Normal Table or technology to find the $z$-score that corresponds to the cumulative area 0.0038. $z=$ $\square$ (Type an integer or decimal rounded to two decimal places as needed.)

Solution

Solution Steps

Step 1: Identify the Cumulative Area

We are given a cumulative area of $ 0.0038 $. This value represents the area under the standard normal curve to the left of a certain z-score.

Step 2: Find the Corresponding z-Score

To find the z-score that corresponds to the cumulative area of $ 0.0038 $, we use the inverse of the cumulative distribution function (CDF) for the standard normal distribution. The calculated z-score is:

\[ z \approx -2.67 \]

Step 3: Round the z-Score

The z-score is rounded to two decimal places, resulting in:

\[ z = -2.67 \]