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Answer :
Final answer:
To find the first quartile, calculate the z-score and use the z-score table to find the corresponding IQ score.
Explanation:
To find the first quartile, we need to calculate the z-score corresponding to the bottom 25% of the distribution. The z-score can be calculated using the formula:
z = (X - μ) / σ
where X is the IQ score, μ is the mean, and σ is the standard deviation.
After calculating the z-score, we can use the z-score table to find the corresponding IQ score. The first quartile (Q1) is the value separating the bottom 25% from the top 75% of the distribution.
In this case, since the mean is 98.1 and the standard deviation is 19, we can calculate the z-score as follows:
z = (Q1 - 98.1) / 19 = -0.674
From the z-score table, we find that the corresponding percentile is 0.2500. This means that the first quartile IQ score, Q1, is the IQ score that separates the bottom 25% from the top 75% of the distribution.
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