Z SCORE math


 CJ 301


Assignment #5






–Please answer each of the following questions. Also, INTERPRET your answers.


You must use the lecture for this week while working on this assignment


– Z score module – under the Learning Modules. (Also, use the Z score table).





 *20 points total




YOUR NAME: _______________________________________________






  1. A state department of corrections has a policy whereby it accepts as correctional officers only those who score in the top 5 % of a qualifying exam. (4 points)




The mean of this test is 80.


Standard deviation is 10.






Would a person with a raw score of 95 be accepted?


         (Calculate a Z score: score – mean/st.dev.=   )














  1. Given a normal distribution of raw scores with a mean of 60 and a standard deviation of 10, what proportion of cases fall:




  1. between a raw score of 40 and 80? (3 points)





  2. between a raw score of 45 and 50? (3 points)






  1. Find the z-score corresponding to a raw score of 90 from a normal distribution with mean 60 and standard deviation 8. (2 points)










  1. For a normal distribution where the mean is 50 and the standard deviation is 8, what is the area :






  • Between the scores of 30 and 65? (2 points)




    5. Assume that the distribution of a college entrance exam is normal with a mean of 500 and a standard deviation of 100. For each score below, find the equivalent Z score, the percentage of the area above the score, and the percentage of the area below the score. (3 + 3 points)


    Score                            Z score                    % Area Above         % Area Below


    a) 375



    b) 437


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