Question

In a school district, the scores on a test given to all freshmen are normally distributed with a mean of 70 and a standard deviation of 8. If a student's score is 84, what is the z-score for that student's performance?

A) z=1
B) z=2
C) z=1.5
D) z=0.5

Answer 1

The z-score for a student's test score of 84 is calculated using the formula z = (X - μ) / σ, which equals (84 - 70) / 8. The resulting z-score is 1.75.

Step-by-step explanation:

The problem provided states that a student in a school district scored 84 on a test where the mean score is 70, and the standard deviation is 8. The question asks for the z-score for that student's performance. To calculate the z-score, we use the formula:

z = (X - μ) / σ

Where:

• X is the score of interest (84 in this case)
• μ (mu) is the mean score (70)
• σ (sigma) is the standard deviation (8)

Plugging in the values into the formula, we get:

z = (84 - 70) / 8 = 14 / 8 = 1.75

Therefore, the z-score for the student who scored 84 is 1.75, which is not one of the options presented. It appears there may have been a mistake in the options given, as none of them correctly match the calculated z-score.