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.)
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Solution

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Solution Steps

Step 1: Understanding the Problem

We need to find the z-score that corresponds to a cumulative area of 0.11420.1142 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)=0.1142P(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 0.11420.1142 is:

z=1.20 z = -1.20

Final Answer

The z-score that corresponds to the cumulative area 0.11420.1142 is

z=1.20 \boxed{z = -1.20}

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