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The problem asks for the z-score that corresponds to an area of \( 0.7418 \) to the left of \( z \) in a standard normal distribution.

To find the \( z \)-value that corresponds to an area of \( 0.7418 \):
1. **Use the cumulative distribution function (CDF)** of the standard normal distribution.
2. Look up \( 0.7418 \) in a z-table, or use a calculator to find the z-score such that \( P(Z < z) = 0.7418 \).

Using a z-table or calculator:
- The closest area to \( 0.7418 \) corresponds approximately to a \( z \)-score of \( 0.65 \).

So, \( z \approx 0.65 \).

Would you like more details on how to use the table or calculator for this? 

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Here are some additional questions to explore:
1. What is a z-score and how is it used in probability?
2. How do you interpret areas under the normal curve?
3. Why is the area to the left of the z-score significant in statistics?
4. What would be the z-score for an area of \( 0.85 \)?
5. How do you calculate probabilities for z-scores not listed in a table?

**Tip:** Remember, for any given area in the standard normal distribution, a z-table or calculator can help find the exact corresponding z-score.

Find the z value that corresponds to an area of 0.7418 to the left of z in a standard normal distribution.

Learn how to find the z-score that corresponds to an area of 0.7418 to the left of z in a standard normal distribution. This problem covers key statistical concepts, including z-scores and the cumulative distribution function (CDF). Suitable for students in Grades 11-12.

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