High School

Assume that adults have IQ scores that are normally distributed with a mean of 100.2 and a standard deviation of 22.4.

Find the first quartile (Q1), which is the IQ score separating the bottom 25% from the top 75%.

A. 85.6
B. 90.4
C. 92.2
D. 95.8

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):

  1. Calculate the Z-score for the first quartile using the formula: Z = (Q1 - Mean) / Standard Deviation.
  2. Find the Z-score that corresponds to the first quartile, which is approximately -0.6745.
  3. 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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