Question
Which of the following percentages accurately estimates the area under a normal curve between a z-score of -0.11 and 2.43?
A. 53.63 percent
B. 45.62 percent
C. 99.25 percent
D. 54.38 percent
A. 53.63 percent
B. 45.62 percent
C. 99.25 percent
D. 54.38 percent
Answers
GPT-4o mini
To find the area under a normal curve between a z-score of -0.11 and 2.43, we need to look up the cumulative probabilities for these z-scores in the standard normal distribution table (or use a calculator).
1. **Z-score of -0.11**: The cumulative probability corresponding to a z-score of -0.11 is approximately 0.4562.
2. **Z-score of 2.43**: The cumulative probability corresponding to a z-score of 2.43 is approximately 0.9925.
To find the area between these two z-scores, we subtract the cumulative probability for -0.11 from the cumulative probability for 2.43:
\[
\text{Area} = P(Z < 2.43) - P(Z < -0.11) \\
\text{Area} = 0.9925 - 0.4562 = 0.5363
\]
To convert this area into a percentage, we multiply by 100:
\[
0.5363 \times 100 = 53.63\%
\]
Therefore, the percentage that accurately estimates the area under the normal curve between a z-score of -0.11 and 2.43 is:
**A. 53.63 percent**.
1. **Z-score of -0.11**: The cumulative probability corresponding to a z-score of -0.11 is approximately 0.4562.
2. **Z-score of 2.43**: The cumulative probability corresponding to a z-score of 2.43 is approximately 0.9925.
To find the area between these two z-scores, we subtract the cumulative probability for -0.11 from the cumulative probability for 2.43:
\[
\text{Area} = P(Z < 2.43) - P(Z < -0.11) \\
\text{Area} = 0.9925 - 0.4562 = 0.5363
\]
To convert this area into a percentage, we multiply by 100:
\[
0.5363 \times 100 = 53.63\%
\]
Therefore, the percentage that accurately estimates the area under the normal curve between a z-score of -0.11 and 2.43 is:
**A. 53.63 percent**.