Determine the area under the standard normal curve that lies to the right of left parenthesis a right parenthesis Upper Z equals negative 1.89 comma(a) Z=−1.89, ​(b) Upper Z equals 1.83 commaZ=1.83, ​(c) Upper Z equals negative 0.12 commaZ=−0.12, and​ (d) Upper Z equals negative 1.14 .Z=−1.14.
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Part 1
​(a) The area to the right of Zequals=negative 1.89−1.89 is enter your response here.
​(Round to four decimal places as​ needed.)
Part 2
​(b) The area to the right of Zequals=1.831.83 is enter your response here.
​(Round to four decimal places as​ needed.)
Part 3
​(c) The area to the right of Zequals=negative 0.12−0.12 is enter your response here.
​(Round to four decimal places as​ needed.)
Part 4
​(d) The area to the right of Zequals=negative 1.14−1.14 is enter your response here.
​(Round to four decimal places as​ needed.)

To determine the area under the standard normal curve to the right of a given Z-score, we need to use a **Z-table** (standard normal distribution table). This table provides the cumulative area to the left of the Z-score. The area to the right can be found by subtracting this cumulative area from 1.

### Part 1: \( Z = -1.89 \)

1. Find the cumulative area to the left of \( Z = -1.89 \) using the Z-table.
2. According to the Z-table, the cumulative area is approximately **0.0294**.
3. The area to the right of \( Z = -1.89 \) is:
   \[
   1 - 0.0294 = 0.9706
   \]
   So, the area to the right of \( Z = -1.89 \) is **0.9706**.

---

### Part 2: \( Z = 1.83 \)

1. Find the cumulative area to the left of \( Z = 1.83 \) using the Z-table.
2. According to the Z-table, the cumulative area is approximately **0.9664**.
3. The area to the right of \( Z = 1.83 \) is:
   \[
   1 - 0.9664 = 0.0336
   \]
   So, the area to the right of \( Z = 1.83 \) is **0.0336**.

---

### Part 3: \( Z = -0.12 \)

1. Find the cumulative area to the left of \( Z = -0.12 \) using the Z-table.
2. According to the Z-table, the cumulative area is approximately **0.4522**.
3. The area to the right of \( Z = -0.12 \) is:
   \[
   1 - 0.4522 = 0.5478
   \]
   So, the area to the right of \( Z = -0.12 \) is **0.5478**.

---

### Part 4: \( Z = -1.14 \)

1. Find the cumulative area to the left of \( Z = -1.14 \) using the Z-table.
2. According to the Z-table, the cumulative area is approximately **0.1271**.
3. The area to the right of \( Z = -1.14 \) is:
   \[
   1 - 0.1271 = 0.8729
   \]
   So, the area to the right of \( Z = -1.14 \) is **0.8729**.

---

### Summary of Areas:
- (a) \( Z = -1.89 \) → Area to the right: **0.9706**
- (b) \( Z = 1.83 \) → Area to the right: **0.0336**
- (c) \( Z = -0.12 \) → Area to the right: **0.5478**
- (d) \( Z = -1.14 \) → Area to the right: **0.8729**

Would you like further details or any clarifications?

### Relative Questions:
1. What is the process for finding the area to the left of a Z-score?
2. How can you interpret the area under a normal distribution curve in terms of probability?
3. Why is the total area under the normal curve always equal to 1?
4. What is the significance of a Z-score in a standard normal distribution?
5. How can Z-scores be used to compare data from different normal distributions?

### Tip:
Always remember that the Z-table typically provides the area to the **left** of the Z-score. For areas to the right, subtract the table value from 1.

Determine the area under the standard normal curve that lies to the right of (a) Z = -1.89, (b) Z = 1.83, (c) Z = -0.12, and (d) Z = -1.14. Round to four decimal places as needed.

Learn how to find the area under the standard normal curve for Z-scores Z = -1.89, Z = 1.83, Z = -0.12, and Z = -1.14. This problem demonstrates how to use Z-tables and provides detailed solutions for each Z-score with step-by-step calculations. Suitable for Grades 10-12 and college-level statistics students.

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