Undergrads Probablity


New Member
Hi, Am I understand the students' score order correctly?
On a psychology exam with m = 76 and = 12, Tom scored 8 points below the mean, Mary had a score of X = 73, and Bill had a z-score of z = –0.50. Place these three students in order from lowest to highest score. Explanation: Tom scored 8 below mean which is 68, 76-8= 68 m=76 Mary’s score is 73. Bill’s score= 70 I use this formula : Z = (X - µ))/(σ ) to transfer Bill’s z-score into a raw score as other students scores to compare them easily. TOM -Student with lowest score( received the lowest scores because he received grade 68 which is 8 scores below the mean) Bill - Student with middle score(he received grade 70 which is 6 scores below) Marry- Student with highest score(she received a highest score of 73 which is only 3 scores below mean). Bill's score z = (x-μ)/s -.50 = (x-76)/12 (-.5)*12 + 76 = x = 70


Super Moderator
Yes, you are essentially correct. However, you can just use the Z-scores: Lowest Tom Z=-0.666, Middle Bill Z=-0.50, Highest Mary Z=-0.25, which are all below the mean. I wonder who's teaching this course.

The Z-score transformation is just a linear transformation.


Ambassador to the humans
You could use z-scores but in this case it's less work to transform the one z-score into a raw score than it is to transform the two raw scores into z-scores.