Extra Statistics Practice:
1) 1) A normal distribution of scores has a standard deviation of 10. Find the z-score corresponding to each
of the following values:
a) A score that is 20 points above the mean.
b) A score 10 points below the mean.
c) A score 15 points above the mean.
d) A score 30 points below the mean.
2) The Wechler Adult Intelligence Test Scale is composed of a number of subtests. On one subtest, the
scores have a mean of 35 and a standard deviation of 6. Assuming the scores form a normal distribution:
a) What number represents the 65th percentile?
b) What number represents the 90th percentile?
c) What is the probability of getting a score between 28 and 38?
d) What is the probability of getting a score between 41 and 44?
3) Scores on the SAT form a normal distribution with =500 and =100.
a) What is the minimum score necessary to be in the top 15% of the SAT distribution?
b) Find the range of values that defines the middle 80% of the distribution of SAT scores.
4) For a normal distribution, find the z-score location that separates the distribution as follows:
a) Separate the highest 30% from the rest of the distribution.
b) Separate the lowest 40% from the rest of the distribution.
c) Separate the highest 75% from the rest of the distribution.
--------------------------------------------------------------------------------------------------------------------------------SOLUTIONS - PRACTICE PROBLEMS – Z SCORES
1) A normal distribution of scores has a standard deviation of 10. Find the z-score corresponding to each of
the following values:
a) A score that is 20 points above the mean. (z = +2.0)
b) A score 10 points below the mean. (z = -1.0)
c) A score 15 points above the mean. (z = +1.5)
d) A score 30 points below the mean. (z = -3.0)
2) The Wechler Adult Intelligence Test Scale is composed of a number of subtests. On one subtest, the
scores have a mean of 35 and a standard deviation of 6. Assuming the scores form a normal distribution:
a) What number represents the 65th percentile? (37.34)
We are looking for the z-score associated with 65% of the curve, so we look for the z that is
goes with 65%. z=0.39 is closest, so we use that. z = (x – μ)/σ  .39 = (x – 35)/6 
x = 37.34
b) What number represents the 90th percentile? (42.68)
Same procedure as above.
c) What is the probability of getting a raw score between 28 and 38? (.5705)
First find z-scores associated with 28 (z=-1.17) and 38 (z=+0.50). Look up the percents
associated with these z-scores and subtract them. You will get0.5705 or 57.05%
d) What is the probability of getting a raw score between 41 and 44? (.0919)
Same procedure as above.
3) Scores on the SAT form a normal distribution with =500 and =100.
a) What is the minimum score necessary to be in the top 15% of the SAT distribution? (604)
To get the top 15% that means we are looking at the a value with 85% below it. Look up the
z-score associated with 85% or .85 and the closest z-score is 1.04. Once you have z, use the
steps in #2a to find x.
b) Find the range of values that defines the middle 80% of the distribution of SAT scores. (372 and
628)
Looking for middle 80% of distribution, therefore 40% either side of mean. Look up z-score
associated with 90% (50% + 40%) and 10% (50% - 40%). The closest z-score is 1.28 and
-1.28. once we have each z-score, we use the same procedure as #2a to find both x values.
4) For a normal distribution, find the z-score location that separates the distribution as follows:
a) Separate the highest 30% from the rest of the distribution. (z=+0.52)
Highest 30% means 70% is below that value. Look up the z-score associated with 70% and
you get z = .52
b) Separate the lowest 40% from the rest of the distribution. (z=-0.25)
Look up the z-score associated with 40% and you get z = -0.25.
c) Separate the highest 75% from the rest of the distribution. (z=-0.67)
Highest 75% means 25% below that value. Look up z-score associated with 25% and you
get z = -0.67
From: PSYCHOLOGY 2910 WINTER 2009
http://dogsbody.psych.mun.ca/2910/Practice%20Problems%20-%20z-scores%20-%20solutions.pdf