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.

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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.

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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.

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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.

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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.