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LESSON 2.3 • Density Curves and the Normal Distribution 107

21. Multiply each score by 4, then add
Extending the Concepts 68 67 22 58 66 67 52 41 45 59 40 35
9:00 A.M . 27 to each score.

21. Quiz time The scores on Ms. Martin’s statistics Class: 44 62 24 66 61 67 46 50 48 60 39 38
quiz had a mean of 12 and standard deviation of 3. 22. (a)
Ms. Martin wants to transform the scores, so they 1:00 P.M . 24 50 55 55 44 44 34 47 68 57 52 64
have a mean of 75 and standard deviation of 12. Class: 66 40 45 60 52 56 38 41 52 40 43 66 9 AM Class 1 PM Class
What transformations should she apply to each test 42 2 4 Lesson 2.3
2
score? Explain your reasoning. (a) Make back-to-back stemplots of the two distri- 3 4

butions of test grades. 985 3 8
Recycle and Review 410 4 001344
(b) Compare the distributions. 865 4 57

22. Rise and shine! (1.4) Mr. Wilder teaches two sec- 23.Did you sleep through lunch? (1.8) Refer to 20 5 0222 KEY: 2|4 represents a student in

tions of Introductory Statistics, and he’s curious 98 5 5567 the 1 PM class who scored 24
.

.
whether the 9:00 a.m class is more alert and pro- Exercise 22 Use the 1.5× IQR rule to determine 210 6 04 points on the first test of the term.
if there are any outliers in the distribution of test
ductive than the class that meets right after lunch 877766 6 668
at 1:00 p.m The table gives the grades (out of 68 grades for the 1:00 p.m . class. (b) The shape of the distribution of the
.
points) for each section on the first test of the term.
(C) 2021 BFW Publishers -- for review purposes only.
test scores for both classes is slightly
skewed to the left. The two classes have
the same median score (51 points). The
distribution of scores for the 9:00 AM
class varies more IQR =( 23.5) than for the
1:00 PM class IQR =( 14.5). There are no
obvious outliers in either distribution.
Lesson 2.3 23. IQR = 56.5– 42 14.5; low outliers <
=
Density Curves and the 42–1.5(14.5) = 20.25; high outliers >
+
= 78.25; because there
56.51.5(14.5)
Normal Distribution are no data values less than 20.25 or
greater than 78.25, this distribution has
no outliers.
L E AR N I N G TAR G E T S

• Use a density curve to model a distribution of quantitative data.
• Identify the relative locations of the mean and median of a distribution from a

density curve. LEARNING T AR GET KEY

• Draw a normal curve to model a distribution of quantitative data.
The problems in the test bank are
keyed to the learning targets using
,
In Chapter 1 we developed graphical and numerical tools for describing distributions
of quantitative data. Our work gave us a clear strategy for exploring data on a single these numbers:
quantitative variable. • 2.3.1

• Always plot your data: make a graph—usually a dotplot, stemplot, or histogram.
• Look for the overall pattern (shape, center, variability) and for striking departures • 2.3.2

such as outliers. • 2.3.3
• Calculate numerical summaries to describe center and variability.

In this lesson, we add one more step to this strategy.

• When there’s a regular overall pattern, use a simplified model called a density curve

to describe it. BELL RINGER
This lesson is another good opportunity
to collect data about your students. Ask
them to count the number of outgoing
text messages they sent yesterday, how
many times they ate fast food last week,
or have them guess their instructor’s age.
03_StarnesSPA4e_24432_ch02_088_153.indd 107 07/09/20 1:55 PM
You can then make a stemplot of the
class data.

LESSON 2.3 • Density Curves and the Normal Distribution 107

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