https://file.aiquickdraw.com/mathbot/file/1729306768093c7sdzqhg.jpg

In the image, you are working on normal distribution problems involving \( Z \)-scores.

### 1st Question:
The statement is \( P(z > 1.4) \), meaning you are asked to shade the region to the right of \( z = 1.4 \) under the standard normal distribution curve. Currently, it seems you have the region to the left of a negative value shaded, which is incorrect for this question.

#### What to do:
- Adjust the shading option to **"Right of a value"**.
- Drag the arrow to the position \( z = 1.4 \) and shade everything to the right of it.

### 2nd Question:
The statement is \( P(z < c) = 0.25 \), meaning you're asked to find the value of \( c \) such that the area to the left of \( c \) under the curve is 0.25. Currently, the arrow is placed at \( z = -1.5 \), which likely corresponds to an area greater than 0.25.

#### What to do:
- Drag the arrow to a value of \( z \) that corresponds to an area of 0.25. This value should be around \( z = -0.674 \), as that corresponds to 25% of the data being to the left.

Would you like detailed steps on how to solve these using the Z-table or normal distribution properties?

### Related Questions:
1. How do you calculate the area under a normal curve using Z-scores?
2. What is the significance of the 0.25 value in normal distributions?
3. How can you use a Z-table to find corresponding areas or Z-scores?
4. Why is the Z-score of 1.4 used in the first problem?
5. How does symmetry of the normal distribution help with probability calculations?

### Tip:
When working with standard normal distribution curves, make sure you understand whether you're shading to the left or right of the Z-score. This can significantly affect your results!

Sketch the region corresponding to the statement P(z > 1.4). Sketch the region corresponding to the statement P(z < c) = 0.25.

Learn how to sketch regions for the standard normal distribution curve based on Z-scores. This problem demonstrates how to shade the area for P(z > 1.4) and find the Z-value that corresponds to an area of 0.25. Suitable for high school statistics students.

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