**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?

**math**

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?

**125**

b.
What score corresponds to the 90th percentile?

**145.60**

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

**103.2
136.80**