Z-score problems


1)    A set of mathematics exam scores has a mean of 70 and a standard deviation of 8.  A set of English exam scores has a mean of 74 and a standard deviation of 16. For which exam would a score of 78 have a higher standing?



2)    For a distribution of raw scores with a mean of 45, the Z-score for a raw score of 55 is calculated to be -2.00. Regardless of the value of the standard deviation, why must this Z-score be incorrect?

Score is above the mean


3)    A distribution of scores has a standard deviation of 10. Find the z-scores corresponding to the following values:

a.     A score that is 20 points below the mean -2

b.     A score that is 10 points below the mean -1

c.     A score that is 15 points above the mean +1.5

d.     A score that is 30 points below the mean -3


4)    In a population of scores a raw score with the value of 83 corresponds to a Z of +1.00 and a raw score of 86 corresponds to a Z of +2.00.  What is the mean and standard deviation of this population?

Mean = 80; standard deviation = 3.0


5)    On a statistics exam, you have a score of 73. If the mean of the exam is 65 would you prefer the standard deviation of the scores to be 8 or 16? Why? 8 because that puts you an entire standard deviation above the mean


6)    A normal distribution has a mean of 120 and a standard deviation of 20. For this distribution

a.     What score separates the top 40% of the scores from the rest?


b.     What score corresponds to the 90th percentile?


c.     What range of scores would form the middle 60% of this distribution?

103.2 136.80