# Expert Answers

1. In an experiment on the effect of exercise on memory, the independent variable is (choose only one answer):

a. Gender of the experimenter

b. Number of hours of exercise

c. Gender of the subjects

d. Recall score on a memory test

e. All of the above

For questions 2 and 3 identify which type of sampling is used.

a. Random

b. Systematic

c. Convenience

d. Stratified

e. Cluster

2. On the day of the last presidential election, a researcher developed an exit poll where specific polling stations were randomly selected and all voters were surveyed as they left.

3. A local news station obtained opinions by interviewing neighbors of a person who was the focus of a news story.

4. For the scores 4, 6, 9, 10, 13, 15, 17, 19, 20, and 22, calculate the 65th percentile using the formula: R = P/100 * (N+1) to compute the rank first, then the percentile (Method 3, in Lane Text).

a. 15.50

b. 16.30

c. 17.10

d. 17.30

e. 17.50

5. Which level of measurement is most appropriate for the years in which U.S. presidents were inaugurated?

a. Ordinal

b. Ratio

c. Nominal

d. Interval

e. Spatial

6. From the graph, select all statements that apply:

a. The mean of distribution A < the mean of distribution B

b. The mean of distribution A the mean of distribution B

c. The standard deviation of distribution B < the standard deviation of distribution A

d. The standard deviation of distribution A < the standard deviation of distribution B

e. None of the above

A researcher collected a sample of ten test scores. Round all answers to two decimal places

and be sure to show your work.

Test

Test Score

1

22.5

2

18.4

3

19.0

4

25.6

5

23.6

6

24.0

7

48.5

8

22.4

9

25.0

10

18.1

7. Compute the mean.

8. Compute the median.

9. Compute the variance.

10. Compute the interquartile range (use formula/process in question #4 to compute the

percentiles).

11. Twenty-five randomly selected students were asked the number of movies they

watched the previous week. The results are as follows:

# of movies

Frequency

Relative Frequency

Cumulative Relative Frequency

0

5

5/25 = 0.20

0.20

1

9

9/25 = 0.36

0.56

2

6

6/25 = 0.24

0.80

3

4

4/25 = 0.16

0.96

4

1

1/25 = 0.04

1.00

a. Construct a histogram of the data.

b. Complete the columns of the chart.

12. Counting without Counting????

Can you figure out how many ways can this hapless graduate student can choose among his beloved professors if the chair of the committee must be a mathematician, and the rest of the committee can be a mix of mathematicians and physicists?

13. A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads?

14. You flip a coin three times. (a) What is the probability of getting heads on only

one of your flips? (b) What is the probability of getting heads on at least one flip?

15. A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow

marble. Two marbles are chosen (without replacement). (a) What is the

probability that one will be green and the other red? (b) What is the probability

that one will be blue and the other yellow?

16. A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11

plums, and 2 mangos.

a. Imagine you stick your hand in this refrigerator and pull out a piece of fruit

at random. What is the probability that you will pull out a pear?

b. Imagine now that you put your hand in the refrigerator and pull out a piece

of fruit. You decide you do not want to eat that fruit so you put it back into the

refrigerator and pull out another piece of fruit. What is the probability that the

first piece of fruit you pull out is a banana and the second piece you pull out is

an apple?

c. What is the probability that you stick your hand in the refrigerator one time

and pull out a mango or an orange?

17. Roll two fair dice. Each die has six faces.

a. List the sample space.

b. Let A be the event that either a three or four is rolled first, followed by an even number. Find P(A).

c. Let B be the event that the sum of the two rolls is at most seven. Find P(B).

d. In words, explain what “P(A|B)” represents. Find P(A|B).

e. Are A and B mutually exclusive events? Explain your answer in one to three complete sentences, including numerical justification.

f. Are A and B independent events? Explain your answer in one to three complete sentences, including numerical justification

18. At a college, 72% of courses have final exams and 46% of courses require research papers. Suppose that 32% of courses have a research paper and a final exam. Let F be the event that a course has a final exam. Let R be the event that a course requires a research paper.

a. Find the probability that a course has a final exam or a research project.

b. Find the probability that a course has NEITHER of these two requirements.

19. Table 3.22 identifies a group of children by one of four hair colors, and by type of hair.

Hair Type Brown Blond Black Red Totals

Wavy 20 5 15 3 43

Straight 80 15 65 12 172

Totals 100 20 80 15 215

Table 3.22

a. Complete the table.

b. What is the probability that a randomly selected child will have wavy hair?

c. What is the probability that a randomly selected child will have either brown or blond hair?

d. What is the probability that a randomly selected child will have wavy brown hair?

e. What is the probability that a randomly selected child will have red hair, given that he or she has straight hair?

f. If B is the event of a child having brown hair, find the probability of the complement of B.

g. In words, what does the complement of B represent?

20. You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $500 prize, two $100 prizes, and four $25 prizes. Find your expected gain or loss.

21. FloridaStateUniversity has 14 statistics classes scheduled for its Summer 2013 term. One class has space available for 30 students, eight classes have space for 60 students, one class has space for 70 students, and four classes have space for 100 students.

a. What is the average class size assuming each class is filled to capacity?

b. Space is available for 980 students. Suppose that each class is filled to capacity and select a statistics student at random. Let the random variable X equal the size of the student’s class. Define the PDF for X.

X P(X)

30 1/14

60 8/14 = 4/7

70 1/14

100 4/14 = 2/7

c. Find the mean of X.

d. Find the standard deviation of X.

22. A school newspaper reporter decides to randomly survey 12 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 18% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. How many of the 12 students do we expect to attend the festivities?

e. Find the probability that at most four students will attend.

f. Find the probability that more than two students will attend.

a. Gender of the experimenter

b. Number of hours of exercise

c. Gender of the subjects

d. Recall score on a memory test

e. All of the above

For questions 2 and 3 identify which type of sampling is used.

a. Random

b. Systematic

c. Convenience

d. Stratified

e. Cluster

2. On the day of the last presidential election, a researcher developed an exit poll where specific polling stations were randomly selected and all voters were surveyed as they left.

3. A local news station obtained opinions by interviewing neighbors of a person who was the focus of a news story.

4. For the scores 4, 6, 9, 10, 13, 15, 17, 19, 20, and 22, calculate the 65th percentile using the formula: R = P/100 * (N+1) to compute the rank first, then the percentile (Method 3, in Lane Text).

a. 15.50

b. 16.30

c. 17.10

d. 17.30

e. 17.50

5. Which level of measurement is most appropriate for the years in which U.S. presidents were inaugurated?

a. Ordinal

b. Ratio

c. Nominal

d. Interval

e. Spatial

6. From the graph, select all statements that apply:

a. The mean of distribution A < the mean of distribution B

b. The mean of distribution A the mean of distribution B

c. The standard deviation of distribution B < the standard deviation of distribution A

d. The standard deviation of distribution A < the standard deviation of distribution B

e. None of the above

A researcher collected a sample of ten test scores. Round all answers to two decimal places

and be sure to show your work.

Test

Test Score

1

22.5

2

18.4

3

19.0

4

25.6

5

23.6

6

24.0

7

48.5

8

22.4

9

25.0

10

18.1

7. Compute the mean.

8. Compute the median.

9. Compute the variance.

10. Compute the interquartile range (use formula/process in question #4 to compute the

percentiles).

11. Twenty-five randomly selected students were asked the number of movies they

watched the previous week. The results are as follows:

# of movies

Frequency

Relative Frequency

Cumulative Relative Frequency

0

5

5/25 = 0.20

0.20

1

9

9/25 = 0.36

0.56

2

6

6/25 = 0.24

0.80

3

4

4/25 = 0.16

0.96

4

1

1/25 = 0.04

1.00

a. Construct a histogram of the data.

b. Complete the columns of the chart.

12. Counting without Counting????

Can you figure out how many ways can this hapless graduate student can choose among his beloved professors if the chair of the committee must be a mathematician, and the rest of the committee can be a mix of mathematicians and physicists?

13. A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads?

14. You flip a coin three times. (a) What is the probability of getting heads on only

one of your flips? (b) What is the probability of getting heads on at least one flip?

15. A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow

marble. Two marbles are chosen (without replacement). (a) What is the

probability that one will be green and the other red? (b) What is the probability

that one will be blue and the other yellow?

16. A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11

plums, and 2 mangos.

a. Imagine you stick your hand in this refrigerator and pull out a piece of fruit

at random. What is the probability that you will pull out a pear?

b. Imagine now that you put your hand in the refrigerator and pull out a piece

of fruit. You decide you do not want to eat that fruit so you put it back into the

refrigerator and pull out another piece of fruit. What is the probability that the

first piece of fruit you pull out is a banana and the second piece you pull out is

an apple?

c. What is the probability that you stick your hand in the refrigerator one time

and pull out a mango or an orange?

17. Roll two fair dice. Each die has six faces.

a. List the sample space.

b. Let A be the event that either a three or four is rolled first, followed by an even number. Find P(A).

c. Let B be the event that the sum of the two rolls is at most seven. Find P(B).

d. In words, explain what “P(A|B)” represents. Find P(A|B).

e. Are A and B mutually exclusive events? Explain your answer in one to three complete sentences, including numerical justification.

f. Are A and B independent events? Explain your answer in one to three complete sentences, including numerical justification

18. At a college, 72% of courses have final exams and 46% of courses require research papers. Suppose that 32% of courses have a research paper and a final exam. Let F be the event that a course has a final exam. Let R be the event that a course requires a research paper.

a. Find the probability that a course has a final exam or a research project.

b. Find the probability that a course has NEITHER of these two requirements.

19. Table 3.22 identifies a group of children by one of four hair colors, and by type of hair.

Hair Type Brown Blond Black Red Totals

Wavy 20 5 15 3 43

Straight 80 15 65 12 172

Totals 100 20 80 15 215

Table 3.22

a. Complete the table.

b. What is the probability that a randomly selected child will have wavy hair?

c. What is the probability that a randomly selected child will have either brown or blond hair?

d. What is the probability that a randomly selected child will have wavy brown hair?

e. What is the probability that a randomly selected child will have red hair, given that he or she has straight hair?

f. If B is the event of a child having brown hair, find the probability of the complement of B.

g. In words, what does the complement of B represent?

20. You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $500 prize, two $100 prizes, and four $25 prizes. Find your expected gain or loss.

21. FloridaStateUniversity has 14 statistics classes scheduled for its Summer 2013 term. One class has space available for 30 students, eight classes have space for 60 students, one class has space for 70 students, and four classes have space for 100 students.

a. What is the average class size assuming each class is filled to capacity?

b. Space is available for 980 students. Suppose that each class is filled to capacity and select a statistics student at random. Let the random variable X equal the size of the student’s class. Define the PDF for X.

X P(X)

30 1/14

60 8/14 = 4/7

70 1/14

100 4/14 = 2/7

c. Find the mean of X.

d. Find the standard deviation of X.

22. A school newspaper reporter decides to randomly survey 12 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 18% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. How many of the 12 students do we expect to attend the festivities?

e. Find the probability that at most four students will attend.

f. Find the probability that more than two students will attend.

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