SOL A.9 Algebra 1
Standard Deviation and Z-Scores
Name: ________________________________________________________ Date: ______________________
Practice: Standard Deviation and Z-Scores
Solve the following. Round each answer to the nearest hundredth, if needed.
1. Use the graph below to answer the questions.
Total Points Scored in the Super Bowl
75
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
69
61
56
65
61
55
56
53
44
39
41
50
46
45
48
38
37
31
31
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
(Source: http://www.superbowlhistory.net/superbowl/scores.php)
a) Identify the following:

= _____________________
 = _____________________  2 = ___________________
b)
What is the z-score for the total points scored in the Super Bowl in 2006? ___________
c)
In how many years did the total number of points scored have a z-score between -0.7 and
1.2? ___________________________
d) In which year (or years) was the z-score for the total points scored approximately 0.5?
SOL A.9 Algebra 1
Standard Deviation and Z-Scores
2. Answer parts a – c below.
a) The average height of a certain group of men is 5’10”. If a man who is 6’4” tall is
approximately 2.14 standard deviations above the mean, what is the standard deviation
for this group of men?
__________________________________
b) How tall (in feet and inches) is a man who is approximately 2.14 standard deviations
below the mean?
___________________
c) Would it be more unusual for a man in this group to be 6’ tall or 5’9” tall? Explain.
3) The average score on a science test was 78 and the standard deviation was 7.86.
a) What is the z-score for a student who scored an 89?
b) What is the z-score for a student who scored a 70?
SOL A.9 Algebra 1
Standard Deviation and Z-Scores
c) What grade did a student earn on the test if her z-score was 0? Explain.
d) What grade did a student earn on the test if his z-score was 2.67?
Use the following information to answer questions 4 - 6.
In one year, the average score for College-Bound Seniors on the Critical Reading portion of the
SAT was 497 with a standard deviation of 114. The average score on the Mathematics portion of
the SAT was 514 with a standard deviation of 117.
(Source:http://professionals.collegeboard.com/profdownload/cbs2011_total_group_report.pdf)
In the same year, the average score on the Reading portion of the ACT was 21.3 with a standard
deviation of 6.2. The average score on the Mathematics portion of the ACT was 21.0 with a
standard deviation of 5.3. (Source: http://nces.ed.gov/programs/digest/d10/tables/dt10_155.asp)
4) If a student scored a 600 on the math portion of the SAT and a 24 on the math portion of the
ACT, which score should he use when applying to college? Explain.
SOL A.9 Algebra 1
Standard Deviation and Z-Scores
5) A student scores a 20 on the reading portion of the ACT. If the tests are similar measures,
what score on the SAT would be similar to a 20 on the ACT?
6) Cindy scored a 500 on the math portion of the SAT and a 19 on the math portion of the ACT.
Which score is better? Explain.
7) A collection of books has an average length of 410 pages with a standard deviation of 136
pages. What is the z-score for a book that has 650 pages?
SOL A.9 Algebra 1
Standard Deviation and Z-Scores
Answers:
1) A) 50.05, 11.99, 143.76
B) -1.59
C) Years in which the total points scored were between 42 and 64 would have a z-score between
-0.7 and 1.2. The total points scored in the Super Bowl were between 42 and 64 in 11 of the years.
D) 1997 and 2011
2) A) 2.8
B) 5’4”
C) It would be more unusual for a man in this group to be 6’ tall. The z-score for 6’ is 0.71 and the
z-score for 5’9” is -0.36. A man who is 6’ tall is more standard deviations away from the mean than a
man who is 5’9” tall making it more unusual.
3) a) 1.40
b) -1.02
c) 78. If a student has a z-score of 0, then her grade is equal to the mean because it is 0 standard
deviations above or below the mean.
d) 99
4) 600 on SAT. Z-score for 600 on the SAT is 0.735 and for the 24 on the ACT is 0.566. Therefore,
his SAT score is higher compared to the average score than his ACT score is.
5) 473
6) Cindy’s score on the SAT is better. The z-score for her SAT score is -0.1197 and for her ACT
score is -0.3774. Her ACT is more standard deviations below the mean, so her SAT score is better.
7) 1.77