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.