Answer :
Final answer:
The first quartile (Q1) of a normally distributed set of adult tQ scores with a mean of 97.9 and a standard deviation of 17.3 is 85.6. This score separates the bottom 25% of scores from the top 75%. This quartile score is calculated using the Z-score table and formula.
Explanation:
The first quartile (Q1 or the 25th percentile) in a data set represents the score below which 25%, or one quarter, of the data falls. When calculating Q1 for a normally distributed data set, we can use the Z-score table. This table tells us that the Z-score for the 25th percentile is approximately -0.67. So, in order to find Q1, we use the formula:
Q1 = Mean + (Z * Standard Deviation)
In this context, the mean is 97.9 and the standard deviation is 17.3. Therefore:
Q1 = 97.9 + (-0.67 * 17.3)
= 85.6 (rounded to one decimal place).
So, a tQ score of 85.6 would separate the bottom 25% of scores from the top 75%.
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