Math 301
Introduction to Probability and Statistics
Fall 2007
Section 001 3:00 to 4:30, M W
Instructor: Dr. Chris Edwards
Classroom: Swart 127
Runger, and Hubele.
Phone: 424-1358 or 948-3969
Office: Swart 123
Text: Engineering Statistics, 4th edition, by Montgomery,
Required Calculator: TI-83, TI-83 Plus, or TI-84 Plus, by Texas Instruments. Other TI
graphics calculators (like the TI-86) do not have the same statistics routines we will be using and
may cause you troubles.
Catalog Description: Elementary probability models, discrete and continuous random
variables, sampling and sampling distributions, estimation, and hypothesis testing. Prerequisite:
Mathematics 172 with a grade of C or better.
Course Objectives: The goal of statistics is to gain understanding from data. This course
focuses on critical thinking and active learning. Students will be engaged in statistical problem
solving and will develop intuition concerning data analysis, including the use of appropriate
technology. Specifically students will develop
•
an awareness of the nature and value of statistics
•
a sound, critical approach to interpreting statistics, including possible misuses
•
facility with statistical calculations and evaluations, using appropriate technology
•
effective written and oral communication skills
Grading: Final grades are based on these 300 points:
Topic
Exam 1
Summaries, Probability
Exam 2
Distributions
Exam 3
Inference
Group Presentations 15 Points Each
Homework
10 Points Each
Points
50 pts.
50 pts.
50 pts.
60 pts.
90 pts.
Tentative Date
October 10
November 12
December 12
Various
Mostly Weekly
Chapters
1-3.4, 3.7
3
4
Final grades are assigned as follows:
270 pts. or more
255 pts. or more
240 pts. or more
225 pts. or more
210 pts. or more
180 pts. or more
179 pts. or less
A (90 %)
AB (85 %)
B (80 %)
BC (75 %)
C (70 %)
D (60 %)
F
Homework: I will collect 3 homework problems approximately once a week. The due dates are
listed on the course outline below. While I will only be grading 3 problems, I presume that you
will be working on many more than just the three I assign. I suggest that you work together in
small groups on the homework for this class. What I expect is a well thought-out, complete
discussion of the problem. Please don't just put down a numerical answer; I want to see how you
did the problem. (You won't get full credit for just numerical answers.) The method you use is
much more important to me than the final answer. To aid in your study groups, I will be
distributing a class roll.
Presentations: There will be four presentations, each worth 15 points. The descriptions of the
presentations are on the Days301 file. I will assign you to your groups for these presentations
randomly, but I want to avoid you having the same members each time. I expect each person in
a group to contribute to the work; you can allocate the work in any way you like. If a group
member is not contributing, see me as soon as possible so I can make a decision about what to
do. The topics are: 1 - Displays (September 19). 2 - Probability (October 8). 3 - Central Limit
Theorem (November 19). 4 - Statistical Hypothesis Testing (December 10).
Office Hours: Office hours are times when I will be in my office to help you. There are many
other times when I am in my office. If I am in and not busy, I will be happy to help. My office
hours for Fall 2007 semester are 10:20 to 11:00, Monday, Wednesday, and Friday and 1:50 to
2:50, Tuesday or by appointment.
Philosophy: I strongly believe that you, the student, are the only person who can make yourself
learn. Therefore, whenever it is appropriate, I expect you to discover the mathematics we will
be exploring. I do not feel that lecturing to you will teach you how to do mathematics. I hope to
be your guide while we learn some mathematics, but you will need to do the learning. I expect
each of you to come to class prepared to digest the day’s material. That means you will benefit
most by having read each section of the text and the Days301 file before class.
My idea of education is definitely not "Teaching is telling and learning is listening". I believe
that you must be active in the learning process to learn effectively. Therefore, I view my job as a
teacher as not telling you the answers to the problems we will encounter, but rather pointing you
in a direction that will allow you to see the solutions yourselves. To accomplish that goal, I will
work to find different interactive activities for us to work on. Your job is to use me, your text,
your friends, and any other resources to become adept at the material. Remember, the goal is to
learn mathematics, not to pass the exams. (Incidentally, if you have truly learned the material,
the test results will take care of themselves.)
Monday
Wednesday
September 3
NO CLASS
September 5 Day 1
Introduction, Random Sampling
Chapter 1
September 10 Day 2
Numerical Summaries
Section 2.1
September 12 Day 3
Graphical Summaries
Sections 2.2 to 2.4
September 17 Day 4
Homework 1 Due
Intro to Probability
Sections 3.1 to 3.3
September 19 Day 5
Presentation 1
Permutations, Combinations
September 24 Day 6
Probability Rules
September 26 Day 7
Homework 2 Due
Trees, Bayes'
October 1 Day 8
Coins, Dice, RV's
Section 3.7
October 3 Day 9
Homework 3 Due
Continuous Distributions
Section 3.4
October 8 Day 10
Presentation 2
Normal
Section 3.5.1
October 10 Day 11
October 15 Day 12
Normal Problems
Section 3.5.1
October 17 Day 13
Gamma
Section 3.5.3
October 22 Day 14
Homework 4 Due
Probability Plots, Binomial
Section 3.6, 3.8
October 24 Day 15
Binomial
Section 3.8
October 29 Day 16
Homework 5 Due
Hypergeometric, Negative Binomial
October 31 Day 17
Normal Approx to Binomial
Section 3.10
November 5 Day 18
Homework 6 Due
Linear Comb., Central Limit Theorem
Section 3.12
November 7 Day 19
More CLT
Section 3.13
Exam 1
November 12 Day 20
November 14 Day 21
m&m’s
Section 4-1
Exam 2
November 19 Day 22
Presentation 3
Intro to Hypothesis Testing
Section 4-3
November 21
NO CLASS
November 26 Day 23
Homework 7 due
Z-Test
Section 4-4
November 28 Day 24
Testing Simulations
Section 4-4
December 3 Day 25
Homework 8 Due
Gosset Simulation
Section 4-5
December 5 Day 26
Proportions
Section 4-7
December 10 Day 27
Homework 9 Due
Presentation 4
Review
December 12 Day 28
Exam 3
Homework Assignments: (subject to change if we discover difficulties as we go)
Homework 1, due September 17
1)
The amount of radiation received at a greenhouse plays an important role in determining
the rate of photosynthesis. Here are some data on incoming solar radiation. Use both
numerical and graphical methods to summarize the data. I don't want to see every
method we've used, but I want to see that you know appropriate summarizing methods.
Briefly explain why your choices were good ones.
6.3
10.2
11.9
2)
3)
6.4
10.6
11.9
7.7
10.6
12.2
8.4
10.7
13.1
8.5
10.7
8.8
10.8
8.9
10.9
9.0
11.1
9.1
11.2
10.0
11.2
10.1
11.4
Consider a sample x1, x2,..., xn and suppose that the values of x and s have been
calculated. Let y i  x i  x and zi  yi /s for all i's. Find the means and s's for the y i ' s
and the zi 's .


Specimens of three different types of rope wire were selected, and the fatigue limit was


determined for each specimen.
Construct a comparative box plot and a plotwith all three

quantile plots superimposed. Comment on the information each display contains. Also
explain which graphical display you prefer for comparing these data sets.
Type 1 350
384
350
391
350
391
358
392
370
370
370
371
371
372
372
Type 2 350
380
354
383
359
388
363
392
365
368
369
371
373
374
376
Type 3 350
379
361
380
362
380
364
392
364
365
366
371
377
377
377
Homework 2, due September 28
1)
If A and B are independent events with P(A) > P(B), P(AB)=.0002 and P(AB)=.03,
find P(A) and P(B).
2)
Three married couples have purchased theater tickets and are seated in a row consisting
of just six seats. If they take their seats in a completely random order, what is the chance
that Jim and Paula (husband and wife) sit in the two seats on the far left? What is the
chance that Jim and Paula sit next to each other?
3)
Three molecules each of four types of molecules are linked together to form a chain. One
such chain is ABCDABCDABCD; another is BCDDAAABDBCC. How many such
chain molecules are there? What is the chance that a randomly selected chain molecule
has all three molecules of each type adjacent, as in AAADDDCCCBBB?
Homework 3, due October 5
1)
In a Little League baseball game, suppose the pitcher has a 50 % chance of throwing a
strike and a 50 % chance of throwing a ball, and that successive pitches are independent
of one another. Knowing this, the opposing team manager has instructed his hitters to not
swing at anything. What is the chance that the batter walks on four pitches? What is the
chance that the batter walks on the sixth pitch? What is the chance that the batter walks
(not necessarily on four pitches)? Note: in baseball, if a batter gets three strikes he is out,
and if he gets 4 balls he walks.
2)
A car insurance company classifies each driver as good risk, medium risk, or poor risk.
Of their current customers, 30 % are good risks, 50 % are medium risks, and 20 % are
poor risks. In any given year, the chance that a driver will have at least one citation is 10
% for good risk drivers, 30 % for medium risk drivers, and 50 % for poor risk drivers. If
a randomly selected driver insured by this company has at least one citation during the
next year, what is the chance that the driver was a good risk? A medium risk?
3)
Using the following cdf, find a) P(X=2)
 0
x 0

.06 0  x  1
.19 1  x  2

.39 2  x  3
F(x)  
.67 3  x  4
.92 4  x  5

.97 5  x  6

6 x
 1
b) P(X>3)
c) P(2≤X≤5)
d) P(2<X<5)
Homework 4, due October 22

1)
Use the following pdf and find a) the cdf b) the mean and c) the median of the
distribution.
1 (4  x 2 ) 1  x  2
f (x)  9
otherwise
 0
2)
Suppose grain size in an aluminum/indium alloy can be modeled with the normal curve
with mean 96 and standard deviation 14. What is the probability that grain size exceeds
100? What is the probability that grain size is between 50 and 75? What interval
includes the central 90 % of all grain sizes?
3)
Suppose the time it takes for Jed to mow his lawn can be modeled with a gamma
distribution using =2 and =.5. What is the chance that it takes at most 1 hour for Jed to
mow his lawn? At least 2 hours? Between .5 and 1.5 hours?

Homework 5, due October 29
1)
Here are the March precipitation values for Minneapolis-St. Paul over a 30 year period:
.77
.96
1.35
1.20
.81
.90
3.00
1.43
1.95
1.62
1.51
2.20
2.81
.32
.52
2.48
1.18
.81
1.74
1.89
4.75
.47
1.20
2.05
3.09
3.37
1.31
2.10
1.87
.59
Construct and interpret a normal probability plot for this data. Then take the square root
of each value and construct and interpret a normal probability plot for the transformed
data. Does it seem reasonable to conclude that the square root of precipitation is
normally distributed? Repeat for the cube root.
2)
Suppose that only 20 % of all drivers come to a complete stop at an intersection having
flashing red lights in all directions when no other cars are visible. What is the chance that
of 20 randomly chosen drivers a) at most 6 will come to a complete stop? b) Exactly 6
will? c) At least 6 will? d) On average, how many of any 20 randomly chosen drivers do
you expect to come to a complete stop?
Homework 6, due November 5
1)
A second stage smog alert has been called in a certain area of Los Angeles county in
which there are 50 industrial firms. An inspector will visit 10 randomly selected firms to
check for violations of regulations. If 15 of the firms are actually violating at least one
regulation, what is the pmf of the number of firms visited by the inspector that are in
violation of at least one regulation? Find the Expected Value and Variance for your pmf.
2)
A couple wants to have exactly two girls and they will have children until they have two
girls. What is the chance that they have x boys? What is the chance they have 4 children
altogether? How many children would you expect this couple to have?
3)
Let X have a binomial distribution with n = 25. For p = .5, .6, and .9, calculate the
following probabilities both exactly and with the normal approximation to the binomial.
a) P(15 ≤ X ≤ 20) b) P(X ≤ 15) c) P(20 ≤ X) Comment on the accuracy of the normal
approximation for these choices of the parameters.
Homework 7, due November 26
1)
There are 40 students in a statistics class, and from past experience, the instructor knows
that grading exams will take an average of 6 minutes, with a standard deviation of 6
minutes. If grading times are independent of one another, and the instructor begins
grading at 5:50 p.m., what is the chance that grading will be done before the 10 p.m.
news begins?
2)
A student has a class that is supposed to end at 9:00 a.m. and another that is supposed to
begin at 9:10 a.m. Suppose the actual ending time of the first class is normally
distributed with mean 9:02 and standard deviation 1.5 minutes. Suppose the starting time
of the second class is also normally distributed, with mean 9:10 and standard deviation 1
minute. Suppose also that the time it takes to walk between the classes is a normally
distributed random variable with mean 6 minutes and standard deviation 1 minute. If we
assume independence between all three variables, what is the chance the student makes it
to the second class before the lecture begins?
3)
A 90 % confidence interval for the true average IQ of a group of people is (114.4, 115.6).
Deduce the sample mean and population standard deviation used to calculate this
interval, and then produce a 99 % interval from the same data.
Homework 8, due December 3
1)
A hot tub manufacturer advertises that with its heating equipment, a temperature of
100°F can be achieved in at most 15 minutes. A random sample of 32 tubs is selected,
and the time necessary to achieve 100°F is determined for each tub. The sample average
time and sample standard deviation are 17.5 minutes and 2.2 minutes, respectively. Does
this data cast doubt on the company's claim? Calculate a P-value, and comment on any
assumptions you had to make.
2)
A sample of 50 lenses used in eyeglasses yields a sample mean thickness of 3.05 mm and
a population standard deviation of .30 mm. The desired true average thickness of such
lenses is 3.20 mm. Does the data strongly suggest that the true average thickness of such
lenses is undesirable? Use  = .05. Now suppose the experimenter wished the
probability of a Type II error to be .05 when  = 3.00. Was a sample of size 50
unnecessarily large?
3)
The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test
whether the true average percentage is 5.5, 16 independent samples are analyzed.
Suppose the distribution is normal with standard deviation .3 and the sample mean is
5.25. Does this indicate conclusively that the average percentage differs from 5.5?
Calculate a P-value and comment on any assumptions you had to make.
Homework 9, due December 10
1)
Fifteen samples of soil were tested for the presence of a compound, yielding these data
values: 26.7, 25.8, 24.0, 24.9, 26.4, 25.9, 24.4, 21.7, 24.1, 25.9, 27.3, 26.9, 27.3, 24.8,
23.6. Is it plausible that these data came from a normal curve? Support your answer.
Now calculate a 95% confidence interval for the true average amount of compound
present. Comment on any assumptions you had to make.
2)
A random sample of 539 households from a certain Midwest city was selected, and it was
found that 133 of these households owned at least one firearm. Calculate and interpret a
95 % confidence interval for the true percentage of households in this city that own at
least one firearm.
3)
Forty percent of a certain population have Type A blood. A random sample of 150 recent
donors at a blood bank shows that 92 had Type A blood. Is there any reason to think that
Type A donors are more or less likely to donate blood? Use  = .01. Would your
conclusion have changed using  = .05?
Return to Chris’ Homepage
Return to UW Oshkosh Homepage
Managed by:
chris edwards
Last updated August 7, 2007