Questions: Use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area 0.1142. 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 0.1142. 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 0.1142. $z=$ $\square$ (Type an integer or decimal rounded to two decimal places as needed.)

Solution

Solution Steps

Step 1: Understanding the Problem

We need to find the z-score that corresponds to a cumulative area of $0.1142$ in the standard normal distribution. The z-score indicates how many standard deviations a value is from the mean.

Step 2: Finding the Z-Score

Using the cumulative area $P(Z < z) = 0.1142$, we can find the corresponding z-score using the inverse of the cumulative distribution function (CDF) for the standard normal distribution.

Step 3: Calculation of the Z-Score

The calculated z-score for the cumulative area $0.1142$ is:

\[ z = -1.20 \]