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This image shows a problem involving the standard normal distribution curve:

1. **Part (a):** You are asked to shade the region under the standard normal curve to the left of \( z = -1.50 \). In this case, you need to shade the area from \( z = -\infty \) (far left) to \( z = -1.50 \), representing the cumulative probability up to that point.

2. **Part (b):** You need to use a table or calculator to find the area under the standard normal curve to the left of \( z = -1.50 \). Using a standard normal distribution table (Z-table), the cumulative probability for \( z = -1.50 \) is approximately 0.0668.

Thus, the area to the left of \( z = -1.50 \) is **0.0668**.

Would you like me to explain how to read the Z-table or discuss the process in more detail?

Here are some follow-up questions:
1. What is the area under the curve for \( z = 0 \)?
2. How do you use a Z-table to find probabilities for other Z-values?
3. What does the shaded area represent in a real-world context?
4. How is the area under the standard normal curve related to probability?
5. How would you calculate the area between two Z-values?

**Tip:** The total area under the standard normal curve is always 1, representing 100% probability.

The standard normal curve is graphed below. Shade the region under the standard normal curve to the left of z = -1.50. Use this table or calculator to find the area under the standard normal curve to the left of z = -1.50, and give the answer to four decimal places.

This problem involves calculating the area under the standard normal curve to the left of Z = -1.50. Learn how to use the Z-table to find the cumulative probability and understand the relationship between Z-values and areas under the curve. Suitable for Grades 10-12.

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