CMS Curriculum Guide 2011-2012
Advanced Functions & Modeling
Unit Title: Statistics and Probability
suggested time: 17 days
Enduring understanding (Big Idea):
Statistics are extremely important in engineering. In environmental engineering, hypothesis testing can be used to determine if a
change of an emission level for a chemical as a significant impact on overall pollution. Also, confidence intervals can be used to help
suggest restrictions on by-product wastes in ground water.
Essential Questions:
 How are statistics used for decision making in business and science?
 What are the limitations of statistics?
Recommended
Days
1 day
Textbook Alignment
0-7 Probability with
Permutations and
Combinations
Geometry 13-4
Simulations
1 day
2 days
2 days
Geometry 13-5
Probabilities of
Independent and
Dependent Events
Geometry 13-6
Probabilities of Mutually
Exclusive Events
Mathematical Objectives
 Find the number of possible
outcomes of an experiment
 Use permutations and
combinations with probability
 Design simulations to estimate
probabilities
 Summarize data from
simulations
 Find the probabilities of
independent and dependent
events
 Find the probabilities of events
given the occurrence of other
events
 Find probabilities of events that
are mutually exclusive and
events that are not mutually
exclusive
 Find probabilities of
complements
Connections to 2003 Standards
1.03 Use theoretical and experimental probability
to model and solve problems
b. Calculate and apply permutations and
combinations
1.03 Use theoretical and experimental probability
to model and solve problems
c. Create and use simulations for probability
models
1.03 Use theoretical and experimental probability
to model and solve problems.
a. Use addition and multiplication principles.
1.03 Use theoretical and experimental probability
to model and solve problems.
a. Use addition and multiplication principles.
Test 1
0-8 Statistics
 Find the measures of center and
spread
 Organize statistical data
1.02 Summarize and analyze univariate data to
solve problems.
c. Determine measures of central tendency and
spread
1 day
e. Interpret graphical displays of univariate data
11-1 Descriptive Statistics
 Identify the shapes of
distribution
1-2 days
1-2 days
f. Compare distributions of univariate data
1.02 Summarize and analyze univariate data to
solve problems.
e. Interpret graphical displays of univariate data
11-2 Probability
Distributions
 Construct and use a probability
distribution
f. Compare distributions of univariate data
1.02 Summarize and analyze univariate data to
solve problems.
CMS Curriculum Guide 2011-2012
Advanced Functions & Modeling
 Construct and use a binomial
distribution
c. Determine measures of central tendency and
spread
1.03 Use theoretical and experimental probability
to model and solve problems
d. Find expected values and determine fairness
 Find the area under the normal
distribution
 Find probabilities for normal
distribution
11-3 The Normal
Distribution
1-2 days
11-4 The Central Limit
Theorem
1-2 days
11-5 Confidence Intervals
1-2 days
11-7 Correlation and
Linear Regression
 Use the Central Limit Theorem
 Find normal approximations of
binomial distributions
 Use the normal distribution to
find confidence intervals
 Use t-distributions to find
confidence intervals
 Measure of linear correlations
 Generate least-squares
regression lines
1-2 days
1 day
Algebra 2 12-1
Experiments, Surveys,
and Observational Studies
Algebra 2 12-2 Statistical
Analysis
1 day
 Evaluate surveys, studies, and
experiments
 Distinguish between correlation
and causation
 Use measures of central
tendency and variation to
compare sets of data
 Explore measures of variation
e. Identify and use discrete random variables to
solve problems
1.02 Summarize and analyze univariate data to
solve problems.
d. Recognize, define, and use the normal
distribution curve
1.02 Summarize and analyze univariate data to
solve problems.
d. Recognize, define, and use the normal
distribution curve
1.02 Summarize and analyze univariate data to
solve problems.
d. Recognize, define, and use the normal
distribution curve
1.01 Create and use calculator-generated models
of linear, polynomial, exponential, trigonometric,
power, and logarithmic functions of bivariate data
to solve problems.
b. Check models for goodness-of-fit; use the most
appropriate model to draw conclusions and make
predictions
1.02 Summarize and analyze univariate data to
solve problems.
a. Apply and compare methods of data collection
1.02 Summarize and analyze univariate data to
solve problems.
b. Apply statistical principles and methods in
sample surveys
Vocabulary:
experiment
sample space
independent events
dependent events
factorial
permutation
combination
statistics
univariate data
measure of central
tendency
population
sample
mean, median, mode
measure of spread
(variation)
range
variance
standard deviation
frequency distribution
class (interval)
relative frequency
class width
cumulative frequency
cumulative relative
frequency
quartiles
five-number summary
interquartile range
outliers
negatively skewed
symmetrical distribution
CMS Curriculum Guide 2011-2012
Advanced Functions & Modeling
positively skewed
resistant statistic
cluster
bimodal distribution
random variable
probability distribution
expected value
binomial experiment
binomial distribution
normal distribution
empirical value
z-value
standard normal
distribution
sampling distribution
standard error of the mean
sampling error
continuity correction
factor
inferential statistics
confidence level
maximum error of
estimate
critical value
t-distribution
Resources:
Glencoe McGraw-Hill (TE) Precalculus
Teacher Works Plus Precalculus
Supplemental material from Glencoe Algebra2 and Geometry
Formal Assessments:
 Quizzes
 Review Quiz (Practice Tests)
 Unit Tests (2)
connected.mcgraw-hill.com
correlation coefficient
residual
least-squares regression
residual plot
interpolation
extrapolation
survey
population
census
sample
biased
unbiased
observational study
experiment
treated group
control group
correlation
causation
parameter
probability model
simulation
Law of Large Numbers
conditional probability
probability tree