Probability and Statistics Journal Entries

 

1.        Read the “Fathom” paper given to you and write a thorough response.  Do not summarize the article!  Your response should include the following:

 

·        Your reaction to the content of the paper.

·        What would this lesson have looked like had Fathom not been used?

·        How might it have been different without the technology?

·        How did Fathom help to make this an effective lesson?

 

2.        Suppose you randomly stopped school-aged children as they entered WalMart and asked, “What grade are you in?”  What type of variable does this question represent?  Explain your reasoning.  What are the observational units?  Suppose you gathered the data below.  Use this information to create a circle graph.

 

Grade

K

1

2

3

4

5

Number

10

20

45

90

10

5

 

3.        Recently, a researcher asked students to provide the number of minutes they spent reading the night before.  In addition, the students reported their grade level.  The data are reported below.  Create a side-by-side stemplot for the data.  What statistical tendency is being exhibited?  Why might this statistical tendency exist?  What is a statistical tendency?

 

Grade

5

5

7

7

7

5

5

7

7

7

Time

28

30

20

20

22

31

33

19

18

16

 

Grade

5

5

7

7

7

7

5

5

7

7

Time

34

32

24

29

22

18

28

32

17

23

 

 

4.        Dr. Rivera believes that teachers who were taught as children using manipulative are more inclined to use manipulatives in their own classrooms.  To test this, she surveyed 50 teachers and asked them the following:

·        When you were a child, did your teachers use manipulatives in order to teach mathematical concepts to you?

·        Do you use manipulatives to teach mathematics concepts to your students?

 

Of the 40 teachers replying “yes” to question #1, 25 answered “yes” to question #2.  Of the remaining 10 teachers, 6 answered “yes” to question #2.

 

  • Use the data provided to create a two-way table.
  • Use the information to create and answer a question that represents marginal information.
  • Use the information to create and answer a question that represents conditional information.

 

5.        Explain how to use snap-cubes and the leveling-off procedure to solve the following problem:  On the first three quizzes, Mary scored 6, 9, and 7 points.  How many points must she score on the fourth quiz in order to have an average of 8 points?

 

6.        Explain in your own words what is meant by the phrase, “The mean is the balance point of a distribution.”  Include with your explanation a sample data set, and an explanation of how the mean balances that particular data set.

 

 

7.        Suppose that you are given the following data set:

·        2, 1, 4, 2, 2, 5, 3, 3, 2, 1

Find two different numbers that can be added to the given data set that change the median but not the mean.  Explain how you chose these two numbers.  (Note: The two numbers do not have to be integers.)

 

8.        a) Create a box plot for the data set below.  Describe the process you use in identifying the 5 numbers used in creating the box plot.  Also, describe how these 5 numbers are identified on the box plot.

·        19, 50, 23, 5, 21, 23, 20, 4, 9, 7

b) Describe how you could use the length of the box in your box plot to estimate visually whether or not 50 represents an outlier.

 

9.        a) In your own words, describe what it means if a person’s test score is within one standard deviation of the mean.

b) Suppose that for a set of test scores the mean is 78 and the standard deviation is 4.3.  What would be the score of a person who scored 2.5 standard deviations above the mean?  Explain your reasoning.

 

10.    a) In your own words, explain what it means for two variables to be positively associated.  Provide an example of a pair of variables that would be positively associated.

b) In your own words, explain what it means for two variables to be negatively associated.  Provide an example of a pair of variable that would be negatively associated.  Note: Your examples should be different from those used in the text or discussed in class.

 

11.    Suppose that your experiment is to flip a coin and then roll a die.  When asked to provide an example of a compound event, Janie replied, “Getting heads on the coin and a 4 on the die.  This is a compound even because it contains information on both the coin and the die.”  Explain to Janie why this actually represents a simple event.  Be sure to include an actual example of a compound event and why this event is a compound event.

 

12.    What is the difference, if any, between experimental and theoretical probability?  Explain your reasoning.

13.    Suppose that 100 teachers at a local school were surveyed as to whether or not they used manipulatives in their mathematics classroom.  These teachers were also classified according to what grade level they taught.  The results of the hypothetical survey are given below:

 

Grades K-2

Grades 3-5

Uses manipulatives

45

10

Does not use manipulatives

15

30

 

 

If one teacher is selected at random from this group of teachers, find the two probabilities below:

Explain how you arrived at your answer.

a)      P(uses manipulatives | Grades K-2 teacher)

b)      P(Grades K-2 teacher | uses manipulatives)

 

14.    James has a map of the continental United States on his wall.  While wearing a blindfold, he is going to throw a dart at the map.  He will then remove his blindfold and record what state his date hits.  (Note: You may assume that James will hit a state and not miss the map.)  Sara believes that the probability of James hitting Georgia is 1/48 because Georgia is one state out of a possible 48 states.  What is wrong with Sara’s idea?  What information is needed in order to actually compute the theoretical probability of James hitting Georgia?

 

15.    a) Explain why “The Sum Game” is not a fair game.  Include with your explanation the theoretical probability of Player 1 and Player 2 winning. 

b) Write a new set of rules for “The Sum Game” so that it is now a fair game.  Explain how you know that the game is now fair.

 

16.    a) Based on the data contained in Journal Entry #13, is it true that the probability that a person uses manipulatives depends on whether or not they teach in Grades K-2 or in Grades 3-5?  Justify your response.

b) In part a, you should have show that the events “uses manipulatives” and “grade-level” were dependent.  Reconstruct the two-way table in Journal Entry #13 so that it describes independent events.  You only need to change the numbers—not the column/row headings.  Verify that the numbers in your two-way table are representative of independent events.

 

17.    Consider the following problem:

You are going to randomly select two people from a group of 100 people.  You know that there are 25 teachers in this group.  What is the probability that the two people selected are teachers?

 

Examine Sammy’s work below:

 

P(both teachers) = P(1st teacher AND 2nd teacher) = (25/100) * (25/100) = (625/10000)

 

Is Sammy’s work correct?  If so, explain how you know this is correct.  If not, explain where Sammy went wrong in his thinking and how to correct his work.

 

18.    Experiment:  There are three bags and you are going to select a colored chip from each bag.  Bag A has 2 red chips and 1 blue chip.  Bag B has 3 green chips and 2 red chips.  Bag C has 5 red chips and 4 blue chips.  Suppose you want to know the probability of getting “at least one red chip.”  In class, we worked this type of problem using the complement of the event “at least one red chip.”  First, what is the complement of this event?  Second, why is it beneficial or necessary to use the complement to solve this probability?