Assume that adults have tQ scores that are normally distributed with a mean of 97.9 and a standard deviation 17.3. Find the first quartie Q 1 . which is the 1Q score separating the bottom 25% from the top 75%. (Hint: Draw a graph.) The first quartile is (Type an integer or decimal rounded to one decimal place as needed.)

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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