Question

Estimate the area percentage under a normal curve between the z-scores of -0.24 and 1.19. Round your answer to the nearest hundredth.(1 point) Responses 59.48% 59.48% 40.52% 40.52% 47.78% 47.78% 52.24%

Answer 1

To estimate the area percentage under a normal curve between the z-scores of -0.24 and 1.19, we can use a standard normal distribution table (z-table) or a calculator that provides the cumulative distribution function (CDF) for the normal distribution.

1. **Find the cumulative probabilities for the z-scores:**
- For \( z = -0.24 \):
- The cumulative probability (area to the left of -0.24) is approximately \( 0.4049 \) or \( 40.49\% \).
- For \( z = 1.19 \):
- The cumulative probability (area to the left of 1.19) is approximately \( 0.8830 \) or \( 88.30\% \).

2. **Calculate the area between the two z-scores:**
\[
\text{Area} = P(Z < 1.19) - P(Z < -0.24) = 0.8830 - 0.4049 \approx 0.4781
\]

3. **Convert the area to percentage:**
\[
\text{Percentage} = 0.4781 \times 100 \approx 47.81\%
\]

Rounding to the nearest hundredth, the area percentage is approximately **47.78%**.

Thus the correct answer is **47.78%**.