Question

Vanessa scored 65 on a language midterm at Loyola, where the grades are roughly symmetric with μ=69 and σ=4.0. What can be inferred about Vanessa's score?

a) Above average
b) Below average
c) Exactly at the mean
d) Standard deviation unclear

Answer 1

Vanessa's score is below average.

Step-by-step explanation:

The z-score is a measure of how many standard deviations a data point is from the mean of a distribution. In this case, Vanessa's z-score can be calculated using the formula: z = (x - μ) / σ, where x is Vanessa's score, μ is the mean, and σ is the standard deviation.

Substituting the given values, we have: z = (65 - 69) / 4.0 = -1.0.

Since the grades are roughly symmetric, a z-score of -1.0 indicates that Vanessa's score is one standard deviation below the mean. Therefore, the answer is b) Below average.