Question

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

99.25 percent
99.25 percent

54.38 percent
54.38 percent

53.63 percent
53.63 percent

45.62 percent

Answer 1

To find the area under a normal curve between a z-score of -0.11 and 2.43, we can use a standard normal distribution table or a calculator that provides cumulative probabilities for normal distributions.

1. **Find the cumulative probability for z = -0.11**:
Using a normal distribution table, the cumulative probability for z = -0.11 is approximately 0.4562 (or 45.62%).

2. **Find the cumulative probability for z = 2.43**:
The cumulative probability for z = 2.43 is approximately 0.9925 (or 99.25%).

3. **Calculate the area between the two z-scores**:
Area between z = -0.11 and z = 2.43 = P(Z < 2.43) - P(Z < -0.11)
= 0.9925 - 0.4562
= 0.5363 (or 53.63%).

Therefore, the correct percentage that accurately estimates the area under the normal curve between a z-score of -0.11 and 2.43 is:

**53.63 percent**.