# Z SCORE math

CJ 301

Assignment #5

Z SCORE

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

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