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.
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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 \( 88.30% \).
- For \( z = -0.24 \):
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Calculate the area between the two z-scores: \[ \text{Area} = P(Z < 1.19) - P(Z < -0.24) = 0.8830 - 0.4049 \approx 0.4781 \]
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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%.