Questions: Find the indicated z-score shown in the graph to the right. The z-score is . (Round to two decimal places as needed.)

Find the indicated z-score shown in the graph to the right. The z-score is . (Round to two decimal places as needed.)
Transcript text: Find the indicated $z$-score shown in the graph to the right. The $z$-score is $\square$ $\square$. (Round to two decimal places as needed.)
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Solution

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Solution Steps

Step 1: Analyze the problem

We are given a standard normal distribution curve with the area to the left of a certain z-score shaded. This shaded area represents the probability of observing a value less than or equal to the z-score. The area is given as 0.2266. We need to find the corresponding z-score.

Step 2: Use the z-table

We need to find the z-score corresponding to a cumulative probability of 0.2266. Since this probability is less than 0.5, the z-score will be negative. Looking up the closest value to 0.2266 in a z-table (or using a calculator or software), we find that the closest probability is 0.2266.

Step 3: Find the z-score

The z-score corresponding to a cumulative probability of 0.2266 is approximately -0.75.

Final Answer

-0.75

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