Question

Four students took a national standardized test for which the mean was 500 and the standard deviation was 100. Their scores were 560, 450, 640, and 530. Determine the z-value for each student.

Answer 1

To get the z-value of the scores of the four students, we are going to use the formula for standard score or z-score.  It is score minus the mean score, then divided by standard deviation.

z= Score (X)-Mean / SD 

To find the z-value of each score, we have to use a Z table.  Using the z-score, we are to look first at the y-axis of the table which will highlight the first two digits of the z-score. Then, the x-axis for the second decimal place of the z-score.

You can use this as reference for the z-table: http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf

Mean= 500SD= 100Scores= 560, 450, 640, 530
For the student who scored 560,z= X-Mean / SDz= 560-500 / 100z= 60 / 100z= 0.6
The score is 0.6 standard deviation above the mean. The z-value is 0.7257 or 72.57%.
For the student who scored 450,z= X-Mean / SDz= 450-500 / 100z= -50 / 100z= -0.5
The score is -0.5 standard deviation above the mean. The z-value is 0.3085 or 30.85%.

For the student who scored 640,z= X-Mean / SDz= 640-500 / 100z= 140 / 100z= 1.4
The score is 1.4 standard deviation above the mean. The z-value is 0.9192 or 91.92%.
For the student who scored 530,z= X-Mean / SDz= 530-500 / 100z= 30 / 100z= 0.3
The score is 0.3 standard deviation above the mean. The z-value is 0.6179 or 61.79%.

Answer 2

Answer:

For the student who scored 560,zvalue is 0.7257 or 72.57%.

For the student who scored 450, zvalue is 0.3085 or 30.85%.

For the student who scored 640, zvalue is 0.9192 or 91.92%.

For the student who scored 530, zvalue is 0.6179 or 61.79%.

Step-by-step explanation: