MAT 130: Beginning Statistics

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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 μ = 2, find P(3).

b. If μ = 0.3, find P(1).

c. If μ = 3/4, find P(3).

d. If μ = 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:

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.