Question

On a statistics exam the mean was 78 and the standard deviation was 10. Determine the standard scores of 2 students whose grades were 93 and 62 respectively

Answer 1

The grade = 93, Standard score = 1.5 and grade = 62,Standard score = -1.6.

To solve this problem

Let's first compute the two student z-scores:

Regarding the student who received a score of 93:

`z_1 = 93 -78/ 10 = 1.5`

Regarding the student who received a 62:

`z_2= 62-78/10 = -1.6`

So, The number of standard deviations that separate each student's score from the mean is shown by these z-scores.

The first student's z-score of 1.5 indicates that they performed 1.5 standard deviations above the mean.

The second student's z-score of -1.6 indicates that they performed 1.6 standard deviations below the mean.