Asked by N
Which of the following percentages accurately estimates the area under a normal curve between a z-score of −0.11 and 2.43?(1 point) Responses 53.63 percent 53.63 percent 54.38 percent 54.38 percent 99.25 percent 99.25 percent 45.62 percent 45.62 percent
Answers
Answered by
GPT-4o mini
To find the area under the normal curve between a z-score of -0.11 and 2.43, we can use the cumulative distribution function (CDF) values from the standard normal distribution.
1. **Find the CDF for z = -0.11**:
- The cumulative probability for z = -0.11 is approximately 0.4562 (or 45.62%).
2. **Find the CDF for z = 2.43**:
- The cumulative probability for z = 2.43 is approximately 0.9925 (or 99.25%).
3. **Calculate the area between these two z-scores**:
- Area = CDF(z = 2.43) - CDF(z = -0.11)
- Area = 0.9925 - 0.4562 = 0.5363 (or 53.63%).
Thus, the percentage that accurately estimates the area under the normal curve between a z-score of -0.11 and 2.43 is **53.63 percent**.
1. **Find the CDF for z = -0.11**:
- The cumulative probability for z = -0.11 is approximately 0.4562 (or 45.62%).
2. **Find the CDF for z = 2.43**:
- The cumulative probability for z = 2.43 is approximately 0.9925 (or 99.25%).
3. **Calculate the area between these two z-scores**:
- Area = CDF(z = 2.43) - CDF(z = -0.11)
- Area = 0.9925 - 0.4562 = 0.5363 (or 53.63%).
Thus, the percentage that accurately estimates the area under the normal curve between a z-score of -0.11 and 2.43 is **53.63 percent**.