Z-Score Practice Worksheet Name _____________________________
1. A normal distribution of scores has a standard deviation of 10. Find the z-scores
corresponding to each of the following values:
a) A score that is 20 points above the mean. z=2
b) A score that is 10 points below the mean. z=-1
c) A score that is 15 points above the mean z=1.5
d) A score that is 30 points below the mean. z=-3
2. The Welcher Adult Intelligence Test Scale is composed of a number of subtests.
On one subtest, the raw scores have a mean of 35 and a standard deviation of 6.
Assuming these raw scores form a normal distribution:
a) What number represents the 65
th
percentile (what number separates the
lower 65% of the distribution)? 37.31
b) What number represents the 90
th
percentile? 42.71
c) What is the probability of getting a raw score between 28 and 38? 57%
d) What is the probability of getting a raw score between 41 and 44? 9%
3. Scores on the SAT form a normal distribution with
and
.
a) What is the minimum score necessary to be in the top 15% of the SAT
distribution? 604
b) Find the range of values that defines the middle 80% of the distribution of
SAT scores (372 and 628). Find the z-scores - -1.28, 1.28
4. For a normal distribution, find the z-score that separates the distribution as
follows:
a) Separate the highest 30% from the rest of the distribution. .52
b) Separate the lowest 40% from the rest of the distribution. .25
c) Separate the highest 75% from the rest of the distribution. -.67