https://file.aiquickdraw.com/mathbot/file/17294842024536ldbopul.jpg

The image shows a standard normal distribution with a shaded area to the left of the vertical line labeled "z". The shaded area corresponds to a probability of 0.2546.

To find the indicated \( z \)-score, we need to determine the \( z \)-value that corresponds to a cumulative probability (area under the curve) of 0.2546. This cumulative probability represents the area under the standard normal curve to the left of the \( z \)-value.

Using a standard normal distribution table (Z-table) or a calculator:

- Look for the cumulative probability closest to 0.2546 in the Z-table, which corresponds to a \( z \)-value of approximately **-0.66**.

Thus, the indicated \( z \)-score is \( \boxed{-0.66} \).

Let me know if you need further clarification or details!

Here are 5 relative questions:
1. What does the \( z \)-score represent in a standard normal distribution?
2. How do you calculate the area under a normal distribution curve for a given \( z \)-score?
3. What is the relationship between \( z \)-scores and probability in a normal distribution?
4. Can the standard normal distribution be used for non-normal data?
5. How can you use the Z-table to find areas for both left and right tail probabilities?

**Tip**: Always remember that a negative \( z \)-score means the value is below the mean, while a positive \( z \)-score means it is above the mean.

Find the indicated z-score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. The shaded area corresponds to 0.2546.

Learn how to find the indicated z-score for a standard normal distribution where the area to the left of z is 0.2546. This problem explores the use of cumulative probabilities from the Z-table and standard normal distribution properties. Suitable for high school or college students studying statistics.

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