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Answer :
Final answer:
To find the first quartile, calculate the Z-score and use it to solve for the IQ score. The first quartile IQ score separating the bottom 25% from the top 75% is approximately 85.6. The correct option is (A).
Explanation:
First Quartile (Q1 Calculation):
- Calculate the Z-score for the first quartile using the formula: Z = (Q1 - Mean) / Standard Deviation.
- Find the Z-score that corresponds to the first quartile, which is approximately -0.6745.
- Substitute the values into the Z-score formula: -0.6745 = (Q1 - 100.2) / 22.4 to solve for Q1, which results in Q1 ≈ 85.6.
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