# Statistics Questions: Z Score

Subject Mathematics Applied Statistics

## Question

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.

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)

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

a) between a raw score of 40 and 80?
b) between a raw score of 45 and 50?

3. Find the z-score corresponding to a raw score of 50 from a normal distribution with mean 30 and standard deviation 10

4. 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?

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.

Score                            Z score                   % Area Above         % Area Below

a) 375
b) 437

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