You are a psychological researcher contracted by a flight school to measure the

Question

You are a psychological researcher contracted by a flight school to measure the "competency" of prospective flight instructors using a standardized screening instrument. You know that the average raw score in the population is µ = 65 and = 6. Based on the testing manual, you know that the developers of this instrument generate a standardized average score of 73 and a standard deviation of 10. Answer the following questions about the scores below.

Catherine’s standardized score is 95. What is her raw score? _____________

Jamie’s standardized score is 50. What is his raw score?    _____________        
AJ’s raw score is 71. What is his standardized score? _________________
Zane’s raw score is 92. What is his standardized score? _________________
      

Explanation / Answer

Z = (X - ) /

a) New Z score = (95 - 73) / 10 = 2.2

Raw score = 2.2 * 6 + 65 = 78.2

b) New Z score = (50 - 73) / 10 = -2.3

Raw score = -2.3 * 6 + 65 = 51.2

c) Old Z score = (71 - 65) / 6 = 1

Standardized score = 1 * 10 + 73 = 83

d) Old Z score = (92 - 65) / 6 = 4.5

Standardized score = 4.5 * 10 + 73 = 118

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