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The question asks us to find the z-score where 10% of the total area is to the left of \( z \).

Since this area (10%) corresponds to 0.10 in the cumulative distribution (left-tail), we can look up this value in the z-table provided in the image.

1. Locate the closest value to 0.10 in the table under the "A" column, which represents the area to the left of \( z \).
2. This area corresponds to \( z \approx -1.28 \), which is the z-score where 10% of the area lies to the left.

Thus, the z-score that best satisfies this condition is:
\[
z = -1.28
\]

Would you like more details, or do you have any other questions?

Here are some related questions for further understanding:
1. How is the z-score used to find probabilities in a normal distribution?
2. What is the relationship between z-scores and standard deviations?
3. How can we interpret a positive vs. a negative z-score?
4. How would you find a z-score if given a different percentile, such as 5%?
5. Why is the normal distribution table symmetrical around zero?

**Tip:** Remember, the z-score represents how many standard deviations away a value is from the mean.

Find the z-score that best satisfies the condition: 10% of the total area is to the left of z.

Learn how to determine the z-score where 10% of the total area lies to the left, using the standard normal distribution table. This example demonstrates key concepts of z-scores and percentiles in statistics, ideal for high school students.

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