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.)
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
Final Answer
The z-score that corresponds to the cumulative area 0.1142 is