High School

Assume that adults have IQ scores that are normally distributed with a mean of 101.2 and a standard deviation of 15.6.

Find the first quartile \( Q_1 \), which is the IQ 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.)

Answer :

Final answer:

The first quartile (Q1) of the IQ scores is approximately 90.8.

Explanation:

To find the first quartile (Q1) of the IQ scores, we need to find the corresponding z-score for the 25th percentile. The 25th percentile corresponds to a cumulative probability of 0.25.

Using the standard normal distribution table or a calculator, we can find that the z-score for a cumulative probability of 0.25 is approximately -0.674.

Now, we can use the formula to convert the z-score back to the original IQ score:

IQ score = z-score * standard deviation + mean

Substituting the values:

IQ score = -0.674 * 15.6 + 101.2

Calculating this, we get:

IQ score ≈ 90.8

Therefore, the first quartile (Q1) of the IQ scores is approximately 90.8.

Learn more about finding the first quartile of a normally distributed data set here:

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