5. Multiple Choice: Which of the following distribution choices for probabilities P₁, P2, P3, P4 are a valid distribution for the amount won by a player. Distribution Choices A B C D E P1 P2 P3 P4 0.1 0.05 0.49 0.35 0.05 0.25 0.05 0.75 0.29 0.36 0.15 0.2 0.01 0.49 -0.050.55 0.17 0.33 0.14 0.36

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New Lottery (Questions 5-6)
Suppose a new lottery randomly selects winners from players who buy a ticket and
pays them $100 with probability p₁, $10 with probability p2, or $1 with probability
P3. Losers get no money.
The distribution of the amounts a player can win is shown as follows
i1234
Wi $100 $10 $1 $0
Pi P1 P2 P3 P4
5. Multiple Choice: Which of the following distribution choices for
probabilities P₁, P2, P3, P4 are a valid distribution for the amount won by a
player.
Distribution
Choices
A
B
с
D
E
P1 P2 P3 P4
0.1 0.05 0.49 0.35
0.05 0.25 0.05 0.75
0.29 0.36 0.15 0.2
0.01 0.49 -0.050.55
0.17 0.33 0.14 0.36
6. Assume that the distribution of the amount won in the new lottery is as given
below. Calculate the mean winning amount.
ixi
Pi
1$100 0.05
2 $10
0.10
3 $1
0.25
4 $0
0.60
Transcribed Image Text:New Lottery (Questions 5-6) Suppose a new lottery randomly selects winners from players who buy a ticket and pays them $100 with probability p₁, $10 with probability p2, or $1 with probability P3. Losers get no money. The distribution of the amounts a player can win is shown as follows i1234 Wi $100 $10 $1 $0 Pi P1 P2 P3 P4 5. Multiple Choice: Which of the following distribution choices for probabilities P₁, P2, P3, P4 are a valid distribution for the amount won by a player. Distribution Choices A B с D E P1 P2 P3 P4 0.1 0.05 0.49 0.35 0.05 0.25 0.05 0.75 0.29 0.36 0.15 0.2 0.01 0.49 -0.050.55 0.17 0.33 0.14 0.36 6. Assume that the distribution of the amount won in the new lottery is as given below. Calculate the mean winning amount. ixi Pi 1$100 0.05 2 $10 0.10 3 $1 0.25 4 $0 0.60
Music and Exam Performance (Questions 7-10)
Researcher believe that 75% of students (or more) can benefit from listening to
music while studying for an exam. To verify this, they recruited 120 high school
students from different grade levels (Freshmen to Senior) to participate in a study.
The students were asked to take a test immediately after they studied a new subject
in a room for three hours. The researchers asked students to repeat the process two
times: once without listening to music and another time while listening to their
preferred music. The order of the tests (with or without music) and the subjects
were randomly assigned.
The researchers recorded the difference between with-music and without-music
scores to measure the impact of listening to music on score. In addition to the
above information, they recorded students' gender.
7. Fill in the following blanks with all applicable variables from the
information provided above.
which is a b.
The response variable in this study is a.
variable.
The explanatory variables are c.
Gender is an example of a d.
A case in this study is e.
dataset.
The population of interest is g.
h.
variable.
and there are f.
cases in the
and the sample used in the study is
8. If 77 of the students scored better in the test that they prepared for while
listening to music, find the proportion of students who can benefit from
listening to music.
9. True or False: The value "75%" stated in the problem is a statistic.
10. True or False: The value "75%" stated in the problem is a parameter.
Transcribed Image Text:Music and Exam Performance (Questions 7-10) Researcher believe that 75% of students (or more) can benefit from listening to music while studying for an exam. To verify this, they recruited 120 high school students from different grade levels (Freshmen to Senior) to participate in a study. The students were asked to take a test immediately after they studied a new subject in a room for three hours. The researchers asked students to repeat the process two times: once without listening to music and another time while listening to their preferred music. The order of the tests (with or without music) and the subjects were randomly assigned. The researchers recorded the difference between with-music and without-music scores to measure the impact of listening to music on score. In addition to the above information, they recorded students' gender. 7. Fill in the following blanks with all applicable variables from the information provided above. which is a b. The response variable in this study is a. variable. The explanatory variables are c. Gender is an example of a d. A case in this study is e. dataset. The population of interest is g. h. variable. and there are f. cases in the and the sample used in the study is 8. If 77 of the students scored better in the test that they prepared for while listening to music, find the proportion of students who can benefit from listening to music. 9. True or False: The value "75%" stated in the problem is a statistic. 10. True or False: The value "75%" stated in the problem is a parameter.
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