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Let's go through the two parts of this problem:

### (a) Sketch the region corresponding to the statement \( P(z < 1.8) \)
This statement refers to the probability that a standard normal random variable \( z \) is less than 1.8. To visualize this, we want to shade the region under the standard normal curve to the left of \( z = 1.8 \).

1. The normal distribution is symmetric around 0.
2. \( z = 1.8 \) is to the right of 0.
3. The area (or probability) under the curve to the left of \( z = 1.8 \) represents \( P(z < 1.8) \).

So, you need to drag the arrow to \( z = 1.8 \) on the graph and shade the region to the left of this value.

### (b) Sketch the region corresponding to the statement \( P(z > c) = 0.2 \)
This statement says that the probability that \( z \) is greater than some value \( c \) is 0.2. This means we are looking for the value \( c \) such that the area under the normal curve to the right of \( c \) is 0.2. To solve this:

1. The area under the curve to the right of \( c \) is 0.2, which means the area to the left of \( c \) must be \( 1 - 0.2 = 0.8 \).
2. From standard normal tables or a calculator, you can find that \( P(z < 0.8416) = 0.8 \), so \( c \approx 0.8416 \).

In your diagram, you need to drag the arrow to \( z = 0.8 \) and shade the region to the right of this value.

Would you like further explanation on how to look up values in the z-table or more details on solving these types of probability problems?

### Related Questions:
1. How do you interpret areas under the normal curve in terms of probabilities?
2. How can you find a specific z-score given a probability?
3. What is the relationship between the z-score and the standard normal distribution?
4. How would the graph change if the mean and standard deviation were different?
5. What tools can you use to calculate areas under the normal distribution?

**Tip**: When working with normal distributions, remember that the total area under the curve always equals 1. This makes it easy to determine areas for complementary probabilities (e.g., \( P(z < c) \) and \( P(z > c) \)).

Sketch the region corresponding to the statement P(z < 1.8) and P(z > c) = 0.2

Learn how to sketch regions under the standard normal curve for P(z < 1.8) and P(z > c = 0.2). This problem covers essential concepts in probability and statistics, including normal distributions, z-scores, and how to calculate areas under the curve.

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