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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### 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
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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