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The problem involves finding the area under the standard normal curve from \( z = -2.37 \) to \( z = 0 \).

This is a standard normal distribution problem where we can look up the cumulative probability for \( z = -2.37 \) and subtract it from the cumulative probability at \( z = 0 \) (which is always 0.5 for a standard normal distribution).

Using a standard normal table or a calculator:

1. The cumulative area to the left of \( z = -2.37 \) is approximately 0.0089.
2. The cumulative area to the left of \( z = 0 \) is 0.5000.

So, the area of the shaded region is:

\[
0.5000 - 0.0089 = 0.4911
\]

Thus, the area of the shaded region is approximately **0.4911**.

Would you like further details or have any other questions? Here are 5 related questions for you:

1. What is the area to the left of \( z = 1.96 \) in the standard normal distribution?
2. How do you calculate the area for a two-tailed test in a normal distribution?
3. What is the significance of the standard normal curve in probability?
4. How do you calculate the z-score for a data point given a mean and standard deviation?
5. How can you use technology (such as a graphing calculator) to find areas under the normal curve?

**Tip:** For standard normal distribution problems, the cumulative area for \( z = 0 \) is always 0.5, as it represents the midpoint of the distribution.

Find the area of the shaded region under the standard normal curve from z = -2.37 to z = 0.

Learn how to calculate the area under the standard normal curve from z = -2.37 to z = 0. This solution uses key statistical concepts such as z-scores and cumulative distribution functions, providing a step-by-step breakdown. Suitable for Grades 11-12 and college-level students.

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