6.1 Normal Distributions
Lecture Notes
Learning Objectives:
Identify distributions as symmetric or skewed.
Identify the properties of a normal distribution.
Find the area under the standard normal distribution, given various z values.
Classroom Example
5.1 Probability Distribution
Lecture Notes
Learning Objectives:
Construct a probability distribution for a random variable.
Classroom Examples:
Do the following examples from the book:
Problems 1, 7, 13, 15, 29, 33; page 266
Homework:
Problems 2, 10, 18,
5.3 The Binomial Distribution
Lecture Notes
Learning Objectives:
Find the exact probability for X successes in n trials of a binomial experiment
Find the mean, variance, and standard deviation for the variable of a binomial
distribution
Classroom Exampl
5.2 Mean, Variance, Standard Deviation, &Expectation
Lecture Notes
Learning Objectives:
Find the Mean, variance, standard deviation, and expected value for a discrete
random variable.
Classroom Examples:
Do the following examples from the book:
Problems
6.4 The Normal Approximation to the Binomial Distribution
Lecture Notes
Learning Objectives:
Use the normal approximation to compute probabilities for a binomial variable.
Classroom Examples:
Suggested classroom examples from the book:
Problems 3, 7, 9.
3.4 Exploratory Data Analysis
Lecture Notes
Learning Objectives:
Use techniques of exploratory data analysis (EDA), including boxplots and fivenumber summaries, to analyze data.
Classroom Examples:
Do the following exercises from the book:
Problems 1, 7,
6.2 Applications of the Normal Distribution
Lecture Notes
Learning Objectives:
Find probabilities for a normally distributed variable by transforming it into a
standard normal variable.
Find specific data values for given percentages, using the standard
3.2 Measures of Variation
Lecture Notes
Learning Objectives:
Describe data using the following measures of variation:
1. the range
2. the variance
3. the standard deviation
Compare the standard deviation of two different variables using the coefficient
3.3 Measures of Position
Lecture Notes
Learning Objectives:
Calculate a z score or standard score.
Identify the position of a data value in a data set using the following measures of
position:
1.
percentiles
2.
deciles
3.
quartiles
Calculate the interq
Healthy Hydration
Drinking water while exercising
Water: Your Essential Nutrient
Cushions and protects vital organs
Transports nutrients and oxygen to cells
Regulates body temperature
Dehydrated body
cannot cool itself
Can cause muscle fatigue and heat st
Calculus I
(Lecture 12 & Lab #12)
Applications of Differentiation [Part 3]
Ziad Z. Adwan
()
Lecture 12 & Lab 12
1 / 36
Learning Objectives
1
Monotone Functions & the 1st Derivative Test .
Motivation for & Denition of Monotone Functions.
Test for Increasin
Calculus I
(Lecture & Lab #9)
Exponential & Logarithmic Functions
Ziad Z. Adwan
()
Lecture & Lab 9
1 / 39
Learning Objectives
1. Exponential Functions.
Denition, Graph, & Properties of Exponential Functions.
The Denition of the Number e and where it comes
Calculus I
(Lecture 11 & Lab #11)
Applications of Differentiation [Part 2]
Ziad Z. Adwan
()
Lecture 11 & Lab 11
1 / 26
Learning Objectives
1
The Mean Value Theorem (MVT) .
Motivation for the Mean Value Theorem.
Rolle Theorem:
s
A Proof using the Extreme-V
Calculus I
(Lecture & Lab #10)
Applications of Differentiation [Part 1]
Ziad Z. Adwan
()
Lecture & Lab 10
1 / 23
Learning Objectives
1. Extrema on an Interval & the Extreme Value Theorem .
Denition of Extrema of a Function on an Interval.
Denition of Abso
Calculus I
(Lecture #8)
Rules for Computation of Derivatives [Part 3]
Ziad Z. Adwan
()
Lecture 8
1 / 30
Learning Objectives
1. The Chain Rule.
Motivation for the Chain Rule.
How to Find Derivatives of Composite Functions.
2. Implicit Dierentiation.
Unders
Calculus I
(Lecture #5)
Introduction to the Derivative of a Function
Ziad Z. Adwan
()
Lecture 5
1 / 26
Learning Objectives
1. The Tangent Line Problem [Revisited].
2. Denition of the Derivative at a Point and in General.
3. Computing the Derivative at a P
Calculus I
(Lecture #7)
Rules for Computation of Derivatives [Part 2]
Ziad Z. Adwan
()
Lecture 7
1 / 23
Learning Objectives
1. The Product Rule.
2. The Quotient Rule.
3. Derivatives of Trigonometric Functions.
4. Higher Order Derivatives.
5. Rates of Chan
Calculus I
(Lecture #6)
Rules for Computation of Derivatives [Part 1]
Ziad Z. Adwan
()
Lecture 6
1 / 20
Learning Objectives
1. The Constant Rule.
2. The Power Rule.
3. The Constant Multiple Rule.
4. The Sum and Dierence Rules.
5. Derivatives of Sine and C
Calculus I
(Lecture #2)
Limits of Functions
Ziad Z. Adwan
()
Lecture 2
1 / 20
Learning Objectives
1. Understanding the Concept of a Limit.
2. Limits which Fail to Exist.
3. Rules for Computing Limits.
4. Limits Involving Innity & Asymptotes.
Ziad Z. Adwan
Calculus I
(Lecture #1)
Preparation for Calculus
Ziad Z. Adwan
()
Lecture 1
1 / 10
Learning Objectives
1. The Tangent Line Problem
2. The Area Problem.
3. Lengths of Curves.
Ziad Z. Adwan
()
Lecture 1
2 / 10
The Tangent Line Problem
Ziad Z. Adwan
()
Lectu
Domain of composite function example:
Domain for : Step 1 Domain for is all x so that x + 10
So we need .
Step 2 Output for g becomes input for f so we must find the range of g.
Graph g to see that range of g is . Step 3 Find domain of f. All x so that
Th
Notes for Section 5.6
Find a polynomial of degree 6 whose coefficients are real numbers and has the zeros 2, -3, 2i,
1-2i.
By the Conjugate Pairs Theorem, since 2i is a zero, then -2i is too and since 1 2i is a zero,
then 1 + 2i is as well. This gives us