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!