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

45.62 percent
45.62 percent

54.38 percent
54.38 percent

53.63 percent
53.63 percent

99.25 percent
99.25 percent

Answer 1

To find the area under a normal curve between a z-score of -0.11 and 2.43, we can use the cumulative distribution function (CDF) for the standard normal distribution.

1. First, look up the cumulative probability for each z-score using standard normal distribution tables or a calculator.

- For a z-score of -0.11:
- The cumulative probability is approximately 0.4562 (or 45.62%).

- For a z-score of 2.43:
- The cumulative probability is approximately 0.9925 (or 99.25%).

2. To find the area between these two z-scores, subtract the cumulative probability of -0.11 from that of 2.43:
\[
\text{Area} = P(Z < 2.43) - P(Z < -0.11) = 0.9925 - 0.4562 = 0.5363 \text{ or } 53.63\%.
\]

So, the area under the normal curve between a z-score of -0.11 and 2.43 is approximately 53.63 percent. The correct response is:

**53.63 percent**