Assume that adults have IQ scores that are normally distributed with a mean of 101 and a standard deviation of 15. Find the third quartile Q,, which is the IQ score separating the top 25% from the others. Click to view page 1 of the table. Click to view page 2 of the table. The third quartile, Q3, is (Round to one decimal place as needed.)
Assume that adults have IQ scores that are normally distributed with a mean of 101 and a standard deviation of 15. Find the third quartile Q,, which is the IQ score separating the top 25% from the others. Click to view page 1 of the table. Click to view page 2 of the table. The third quartile, Q3, is (Round to one decimal place as needed.)
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
- [Page 2 of Z-score Table](#)
- Look up the Z-score that corresponds to the 75th percentile (since \(Q_3\) is the point that separates the top 25% from the others).
2. **Apply the Z-Score Formula:**
- Use the Z-score formula:
\[
Z = \frac{X - \mu}{\sigma}
\]
where \(X\) is the score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
- For the 75th percentile (using Z-score tables), \(Z\) approximately equals 0.675.
3. **Rearrange the Formula to Solve for \(X\):**
- Substitute \(Z\), \(\mu\) (mean = 101), and \(\sigma\) (standard deviation = 15) into the formula:
\[
X = Z \cdot \sigma + \mu
\]
4. **Calculate \(Q_3\):**
- Calculate as follows:
\[
Q_3 = 0.675 \times 15 + 101 = 10.125 + 101 = 111.125
\]
**Answer:**
The third quartile, \(Q_3\), is **111.1** (rounded to one decimal place).
**Note:**
Enter your answer in the provided answer box and then click "Check Answer."
**Diagram/Graph Explanation:**
In this specific task, there are no diagrams or graphs provided. The instructions direct the user to utilize Z-score tables available via the provided links to find the appropriate Z-score corresponding to the 75th percentile.
**Further Instructions:**
Make](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbedd374-d5ca-41f2-a379-751fa7b6bb2f%2Fdf36279f-e92b-49bf-b62d-e7f040aaf4de%2Fko9fez.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining the Third Quartile of IQ Scores
**Problem Statement:**
Assume that adult IQ scores are normally distributed with a mean of 101 and a standard deviation of 15. The task is to find the third quartile (\(Q_3\)), which is the IQ score separating the top 25% from the others.
**Procedure:**
To find the third quartile (\(Q_3\)), you can follow these steps:
1. **Utilize Z-Score Tables:**
- Click the links provided to access the Z-score tables:
- [Page 1 of Z-score Table](#)
- [Page 2 of Z-score Table](#)
- Look up the Z-score that corresponds to the 75th percentile (since \(Q_3\) is the point that separates the top 25% from the others).
2. **Apply the Z-Score Formula:**
- Use the Z-score formula:
\[
Z = \frac{X - \mu}{\sigma}
\]
where \(X\) is the score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
- For the 75th percentile (using Z-score tables), \(Z\) approximately equals 0.675.
3. **Rearrange the Formula to Solve for \(X\):**
- Substitute \(Z\), \(\mu\) (mean = 101), and \(\sigma\) (standard deviation = 15) into the formula:
\[
X = Z \cdot \sigma + \mu
\]
4. **Calculate \(Q_3\):**
- Calculate as follows:
\[
Q_3 = 0.675 \times 15 + 101 = 10.125 + 101 = 111.125
\]
**Answer:**
The third quartile, \(Q_3\), is **111.1** (rounded to one decimal place).
**Note:**
Enter your answer in the provided answer box and then click "Check Answer."
**Diagram/Graph Explanation:**
In this specific task, there are no diagrams or graphs provided. The instructions direct the user to utilize Z-score tables available via the provided links to find the appropriate Z-score corresponding to the 75th percentile.
**Further Instructions:**
Make
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