Question

The grades on a math midterm at Springer are roughly symmetric with μ = 68 and σ = 4.5. Brandon scored 71 on the exam. Find the z-score for Brandon's exam grade. Round to two decimal places.

Answer 1

Brandon's z-score for his midterm grade is 0.67, indicating that he scored 0.67 standard deviations above the mean.

Step-by-step explanation:

To find Brandon's z-score for his math midterm grade, we use the formula for calculating z-scores which is z = (X - μ) / σ. Where:

• X is Brandon's score,
• μ is the mean score of the midterm,
• σ is the standard deviation.

Plugging in the values we have:

z = (Brandon's score - mean score) / standard deviation

z = (71 - 68) / 4.5

z = 3 / 4.5

z = 0.666...

To two decimal places, Brandon's z-score is 0.67.

This means Brandon scored 0.67 standard deviations above the mean on his exam.