https://file.aiquickdraw.com/mathbot/file/1729092190289tabd8h8g.jpg

Let me walk you through answering the questions based on the data in the image.

### Given Information:
- **Mean** of the scores = 37.794
- **Standard deviation (stdev)** = 13.573
- **Number of students (n)** = 34
- **Range of scores**: minimum = 13, maximum = 68
- **Median** score = 34.5
- **Interquartile Range**: Q1 = 30, Q3 = 46
- **Shapiro-Wilk p-value** = 0.1547, indicating normality.

### Answers to Questions:
#### **2.01 How many students took Quiz #1?**
- There are 34 students who took Quiz #1 (n = 34).

#### **2.02 What was the average score for the class for Quiz #1?**
- The average score is the **mean**, which is **37.794**.

#### **2.03 What was the median score for Quiz #1?**
- The median score is **34.5**.

#### **2.04 What was the standard deviation for Quiz #1?**
- The standard deviation is **13.573**.

#### **2.05 What was the variance for Quiz #1?**
- Variance is the square of the standard deviation. Therefore:
  \[
  \text{Variance} = (13.573)^2 = 184.23
  \]

#### **2.06 What was the maximum score for Quiz #1?**
- The maximum score is **68**.

#### **2.07 The histogram of the scores is shown to the right. Does the shape appear "bell-shaped"?**
- Yes, the histogram, with a normal curve overlay, appears roughly bell-shaped.

#### **2.08 What is the z-score for the raw score of 68?**
The formula for z-score is:
\[
z = \frac{X - \mu}{\sigma}
\]
Where:
- \(X = 68\) (raw score)
- \(\mu = 37.794\) (mean)
- \(\sigma = 13.573\) (standard deviation)

\[
z = \frac{68 - 37.794}{13.573} = \frac{30.206}{13.573} \approx 2.23
\]
So, the z-score for a raw score of 68 is approximately **2.23**.

#### **2.09 How many standard deviations is the score of 68 away from the mean (average) score?**
- The score of 68 is approximately **2.23 standard deviations** above the mean.

#### **2.10 What is the z-score for the raw score of 37?**
\[
z = \frac{37 - 37.794}{13.573} = \frac{-0.794}{13.573} \approx -0.06
\]
So, the z-score for a raw score of 37 is approximately **-0.06**.

#### **2.11 How many standard deviations is the score of 37 away from the mean (average) score?**
- The score of 37 is approximately **0.06 standard deviations** below the mean.

#### **2.12 How many Course Points did the raw score of 58 earn?**
- To find the z-score for 58:
\[
z = \frac{58 - 37.794}{13.573} = \frac{20.206}{13.573} \approx 1.49
\]
From the table on the right, a z-score of 1.04 to 1.65 corresponds to **28 course points**.

#### **2.13 How many Course Points did the raw score of 37 earn?**
- The z-score for 37 is approximately -0.06, which falls between -0.25 and 0.25. According to the table, this corresponds to **24 course points**.

Would you like any further clarification or details on any of these solutions?

### Follow-Up Questions:
1. How is the variance related to the standard deviation?
2. What does the z-score tell you about a specific student's performance relative to the class?
3. How would you calculate the z-score for a raw score of 50?
4. What might you infer from a student having a negative z-score?
5. How does the shape of the histogram relate to normal distribution?

#### Tip:
To easily interpret z-scores, remember that a score near zero means the raw score is close to the mean, while larger positive or negative z-scores indicate the score is far from the mean in respective directions.

Various questions about Quiz #1 statistics and z-scores based on the data provided in the image, including calculating average scores, median, standard deviation, variance, z-scores for specific raw scores, and interpreting the histogram.

Explore how to calculate key descriptive statistics like mean, standard deviation, and variance for Quiz #1. Learn how to compute z-scores for raw scores of 68 and 37, and analyze the bell-shaped histogram to interpret class performance. Suitable for college-level statistics students.

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