Normal Curve and Standard Scores: Calculating Z-scores, T-scores, and Percentiles, Exams of Biology

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Chapter 4

Normal Curve and Standard Scores

Z-table use

The Normal Curve Some Practice with z-scores, T-scores, etc.

Standard Scores

2.5 13.5 34 34 13.5 2. s (standard deviation) z-score - 2 - 1 0 1 2 T-score 30 40 50 60 70 Percentile 2.5 16 50 84 97.

S T  score  50  10 * z  score

X X z score

   S

X X T score 10 ( ) 50    

Mean S z-score 0 1 T-score 50 10

Raw (e.g., VO2max, bowling, test score, etc.) ?? ??

Standard Scores

Going from raw score to z-score

S

X X T score

10 ( ) 50

   

S

X X z score

  

S

X X z score

  

Going from T-score to z-score

10 z  score  XT ^50

S

X X T score

10 ( ) 50

   

S

X X z score

  

Going from z-score to raw score

S

X X T score

10 ( ) 50

   

S

X X z score

  

X  X (^) Raw  z  score * ( SRaw )

Going from T-score to raw score

First find the z-score from the T-score then use the z-score formula

10 z  score  XT ^50 * ( ) X  X (^) Raw  z  score SRaw

S

X X z score

  

S

X X T score

10 ( ) 50

   

S

X X

z score

You can use only one formula for EVERYTHING.

Just be certain to use the correct and S.

z-score = 0; s = 1

T-score = 50; s = 10

Raw score = ??; s = ??

X

X

X

X