ALLIED MAT130 MODULE 3 HOMEWORK ASSIGNMENT

Homework Assignment IntroductionWelcome to the Module 3 Homework Assignment for MAT 130: Beginning Statistics.This section prepares you to complete this assignment successfully. Please follow these instructions to complete and submit this assignment.You will create a document in either a .doc or .rtf format to record and save your work. If you have never created documents in an .rtf format, please visit the Academic Resource Center and click on Tutorials. You will then see a list of tutorials on the following page. Click on RTF Tutorial.Read the instructions carefully and review your work before you submit your assignment.Include a title page with this assignment. Your title page should follow standard APA formatting. Please view the .allied.edu/Pages/ViewPage.aspx?GroupID=189″>Title Page Example.When you are ready to submit the assignment, click the Start button at the bottom of the page to access the submission page and follow the instructions.Running head: [INSERT
TITLE HERE]

[INSERT
TITLE HERE]
Student
Name
Allied
American University

Author
Note
This
paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught
by [INSERT INSTRUCTOR’S NAME].

PART
I: SHORT RESPONSE

Directions: Please answer each of the following questions thoroughly.

1. The 110th Congress of
the United States included 84 male Senators and 16 female Senators.
a.
If one of these Senators is
randomly selected, what is the probability that a woman is selected?
b.
Does this probability agree
with a claim that men and women have the same chance of being elected as
Senators?

2. When two dice are
rolled, the total is between 2 and 12 inclusive. A student simulates the rolling of two dice
by randomly generating numbers between 2 and 12.
a.
What is the probability of the
student rolling a total of 7 on two dice?
b.
What is the probability of
randomly generating a 7 from the numbers 2 to 12 inclusive?
c.
Does this simulation behave in
a way that is similar to actual dice?
Why or why not? Use your answers from part (a) and (b) in your
explanation.

3. What is the basic
difference between a situation requiring application of the permutations rule
and one that requires the combinations rule?

4. Credit card numbers
typically have 16 digits, but not all of them are random. Answer the following
and express probabilities as fractions.
a.
What is the probability of
randomly generating 16 digits and getting your MasterCard number?
b.
Receipts often show the last
four digits of a credit card number. If those last four digits are known, what
is the probability of randomly generating the other digits of your MasterCard
number?
c.
Discover cards begin with the
digits 6011. If you also know the last four digits of a Discover card, what is
the probability of randomly generating the other digits and getting all of them
correct? Is this something to worry about?

5. A columnist for the Daily
News in New York City wrote about selecting lottery numbers. He stated that some lottery numbers are more
likely to occur because they haven’t turned up as much as they should, and they
are overdue. Is this reasoning
correct? Why or why not? What principle of probability is relevant
here?

6. The Mega Millions
lottery is run in many states. Winning the jackpot requires that you select the
correct five numbers between 1 and 56 and, in a separate drawing, you must also
select the correct single number between 1 and 46. Find the probability of
winning the jackpot.

7. What is a random
variable? Is it possible for a discrete
random variable to have an infinite number of possible values?

8. What is the difference
between a discrete random variable and a continuous random variable?

9. A friend of the author
buys one lottery ticket every week in one year.
Over the 52 weeks, she counts the number of times that she won
something.
a.
In this context, what is the
random variable?
b.
What are the possible values of
the random variable in this problem?

10. A researcher calculates
the expected value for the number of girls in three births. He gets a result of 1.5. He then rounds the result to 2, saying that
it is not possible to get 1.5 girls when three babies are born. Is this reasoning correct? Explain.

11. In the Illinois Pick 3
lottery game, you pay 50 cents to select a sequence of three digits, such as
233. If you select the same sequence of three digits that are drawn, you win
and collect $250.
a.
How many different selections
are possible?
b.
What is the probability of
winning?
c.
If you win, what is your net
profit?
d.
Find the expected value.

12. In New Jersey’s Pick 4
lottery game, you pay 50 cents to select a sequence of four digits, such as
1332. If you select the same sequence of four digits that are drawn, you win
and collect $2788.
a.
How many different selections
are possible?
b.
What is the probability of
winning?
c.
If you win, what is your net
profit?
d.
Find the expected value.
e.
If you bet 50¢ in Illinois’
Pick 4 game, the expected value is -25¢. Which bet is better: A bet in the
Illinois Pick 4 game or a bet in New Jersey’s Pick 4 game? Explain.

13. The final exam in a
sociology course consists of 100 multiple-choice questions. Each question has 5
possible answers, and only 1 of them is correct. An unprepared student makes
random guesses for all of the answers.
a.
Find the mean and standard
deviation for the number of correct answers for such students.
b.
Would it be unusual for a
student to pass the exam by guessing and getting at least 60 correct answers?
Why or why not?

14. What are the conditions
for using the Poisson distribution?

15. Assume that the Poisson
distribution applies, and proceed to use the given mean to find the indicated
probability.
a.
If ? = 2, find P(3).
b.
If ? = 0.3, find P(1).
c.
If ? = 3/4, find P(3).
d.
If ? = 1/6, find P(0).

PART
II: PROJECT

For
this Module 3 Homework Assignment, please submit your response to the
following:

Document your
progress. Who did you interview? How many people did you interview? If you collected data, please submit it
below. If not, please explain what you
did to contribute to this assignment this past week.

Directions: This assignment is a course-long project whereby you will work on
the project in each module. You will
turn in your completed project at the end of Module 8.

Create a survey question to ask others. The
following are examples or some survey questions:

1.
Choose a random number between
1 and 10 inclusive.
2.
What month of the year does
your birthday fall on? Write the numeric
value from 1 to 12.
3.
How many keys are in your
possession at this time?
4.
How many siblings do you have?

In Module 1, you will submit your survey
question to your instructor for approval.
Once you are notified of its approval, you may begin conducting a survey
using your question.

You will need at least 25 participants and will
need to keep the following record for each person:

a.
Gender
b.
Age
c.
Date surveyed
d.
Survey response

Please also keep a count, if any, non-willing
participants. For example, if you chose
the first survey question, then you might have the following records:

Participant #

Gender

Age

Date Surveyed

Survey Response

1

M

18

12/10/12

5

2

F

42

12/15/12

8

3

M

34

12/17/12

1

In the Module 8 Homework Assignment, you will
be asked to analyze your survey results, so please be sure to begin conducting
your survey as soon as your question is approved. Try getting 5 participants a week to satisfy
the required number of participants.