Z-Scores of Three Individuals. Person

¶ … z-scores of three individuals. Person a received a z-score of 1.0, Person B. received a z-score of 0, and Person C. received a z-score of -1.0. Indicate each individual's score as a T score, CEEB score, IQ score, and approximate percentile score. Once you have indicated these transformed scores, in 1 -- 2 pages, describe why it is possible to easily convert standard scores from one scale to another. Include in your answer the mean and standard deviation of each of the transformed scores and the theoretical rationale for their equivalency.

With T scores "the mean is always 50 and the standard deviation is always 10" (T-scores, 2009, everything2com). So Person a would have a score of 60 (standard deviation 70-50), Person B. A score of 50 (standard deviation 40-60), Person C. A score of 40 (standard deviation 40-50). "To convert T-scores to CEEB (College Entrance Examination Board Scores) the tester need only add a zero…the mean for CEEB scores would be 500, with a standard deviation of 100" (Brown, 1988, p.88). Person a would have a score of 600 (standard deviation 500-700), Person B. A score of 500 (standard deviation 400-600), and Person C. A score of 400 (standard deviation 300-500).

The average IQ score is 100. Given how IQ is normally distributed, "the average (mean) is 100 and that the standard deviation is something like 15 (IQ tests sometimes differ in their standard deviations)" (Jara, 2009). This would suggest that Person a was slightly above average, with an IQ 111-119, Person B. was average with an IQ 91-110 upon average, and Person C. below average with an IQ of 89-90 (Jara, 2009). An approximate percentile scores "indicates a student's relative position in a group in terms of the percentage of students scoring lower. It is calculated by taking the number of students scoring lower divided by the number of students taking the exam and multiplying by 100" (Percentile rank, 2009). So Person a would be in the top 2/3, Person B. The middle 1/3 and Person C. that of 0.