https://file.aiquickdraw.com/mathbot/file/1727668355041ev7upt8b.jpg

The graph shown represents a standard normal distribution, also known as the bell curve. The shaded region appears to represent the cumulative area to the right of \( t = -1.5 \).

To find the area of the shaded region, we need to calculate the cumulative probability from \( t = -1.5 \) onward. This involves the cumulative distribution function (CDF) of the standard normal distribution.

1. First, calculate the cumulative probability for \( t = -1.5 \) using standard normal tables or a calculator.
2. Subtract this value from 1 to find the area of the shaded region.

Let me compute that for you:

The CDF value for \( t = -1.5 \) is approximately 0.0668. Therefore, the area of the shaded region is:

\[
1 - 0.0668 = 0.9332
\]

Thus, the area of the shaded region is approximately **0.933**.

Would you like more details or have any questions?

### Relative Questions:
1. How is the CDF used to calculate areas under the normal curve?
2. Why is the total area under the normal distribution curve equal to 1?
3. How would the shaded region change if the value of \( t \) were different?
4. Can we use the Z-score formula to find values not on the standard normal distribution?
5. How is the standard normal distribution applied in real-life problems?

### Tip:
Always remember that the total area under the standard normal curve equals 1, making it easy to find complementary areas by subtracting from 1.

Find the area of the shaded region to the right of t = -1.5 under the standard normal curve.

Learn how to find the area of the shaded region under the standard normal curve for t ≥ -1.5 using the Cumulative Distribution Function (CDF). The calculated area is approximately 0.933, showing the probability associated with this range.

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