Study Guide
Chapter 2 test
The area under a density curve represents a proportion of all observations. The total area under the
curve is_____1_____
Notice that the mean and the median both lie at the ____center____________ of a symmetric density
curve
____68______% of the numbers in a data set fall within 1 standard deviation of the mean
____95______ % of the numbers in a data set fall within 2 standard deviations of the mean
____99.7______% of the numbers in a data set fall within 3 standard deviations of the mean
If the mean is 50 and the standard deviation is 5, what is the range of scores in which 95% of the data
falls?
40-60
If “x” falls 1 standard deviation to the left of the mean, the z-score is ____-1______ and the proportion
is _____.1587_________
z-score represents how many ______standard deviations_______________ away from the mean you
are
𝑥− µ
=𝑧
𝜎
Find the area under the curve below a z-score of -1.34____.0901________
If you are in the 75th percentile. What percent of the population are you better then? What is
the z-score that corresponds? 75% = .67
If you are in the top 18% of test takers, what percent are you better than? What z-score
corresponds with it? 82% = .92
Find the percent of values that fall above a person who has a z-score of 2.01
.0222
The mean is 20, standard deviation is 3. Find me the percent of scores at are at least 18
.7486
From the previous data, find the percent of scores that fall between 18 and 21
.3779
Draw a normal curve, label the standard deviations if the mean is 100 and a standard deviation
of 8. Also, label the percentages between the standard deviations
To find x: Multiply the _________ and ______________ first. Then _______________ the mean
To find µ: Multiply the ____________ and ______________ first. Then _________________ x
and __________________ -1
To find σ: Subtract_____________________ first. Then ____________________ the z-score
What proportion of the population has a score below 20 if the mean is 25 and the standard
deviation is 5?
.1587
What proportion has scores above 10?
.9987
How high a score must you have in order to be in the top 25% of test takers? 28.35
Find the area representing the following regions
z < -2.03 = .0212
z > -2.03 = .9788
Z > 1.95 = .0256
-2.25 < z < 1.60 = .9330
Complete the chart:
Test
Mean
Score
Z-Score
35
36
91.916
110
Standard
Deviation
4.51
4
6.2
3.37
Clerical Ability
Logical Reasoning
Mechanical Ability
Numerical
Reasoning
Spatial Relations
Verbal Fluency
41
47
97
101.95
1.33
2.75
.82
-2.39
105
82
18
2.05
111
80.216
.33
-.87
The mean test grade was 83. The standard deviation was 3.45. What percent of the students
scored at least an 85?
.2810
The mean test grade is an 85. A student was in the 60 th percentile with a standard deviation of
5. Find the students score?
86.25
A baby was born in the 10th percentile. The mean baby weight is 7.5 lbs, the standard deviation
is 1.5 lbs. Find the baby’s birth weight.
5.58
𝑧=
𝑥− 𝜇
𝜎
Data collected from Gallop states that the average American male has a height of 68 inches, with a
standard deviation of 2.9 inches, and the average American female has a height of 64 inches, with a
standard deviation of 3.2 inches. Both distributions are approximately Normal.
1) What percentile would a man be in if he was 72 inches tall: ______.9162_________________
2) What percentile would a woman be in if she was 60 inches tall: _______.1056_____________
3) How tall would a female have to be to be in the 85th percentile: ________67.328__________
4) What percentile would a woman be in if she was 70 inches tall: _________.9699___________
5) How tall would a male have to be to be in the 45th percentile: _____67.623__________
6) What height for a male would put them in the 30th percentile: __________66.492_______
7) A female with a height of 68 inches would be in what percentile: ______.8944___________
8) What height for a female would put them in the 30th percentile: ___________62.336______