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Statistics Homework

 

1. In her science class, Priscilla read about the growth rate (in centimeters) of two varieties of plants after 20 days. For the data shown below, answer questions a-d.

 

                     Variety 1                                                                    Variety 2

                       20  12  49  38  41  43                                      18  54  62  59  53  25

                       51  52  59  55  53  59                                      13  57  42  54  56  38

                       50  58  35  38  33  32                                      41  36  50  62  45  55

                       43  53

 

                        Variety 1                                                       Variety 2

          

           a.         Mean:                                                              a.         Mean:

 

 

           b.         Median:                                                           b.         Median:

 

 

           c.         Mode:                                                              c.         Mode:

 

 

d.  Construct a stem and leaf display with a central stem with Variety 1 on the left and Variety 2 on the right. Order the leaves with the smallest leaves closest to the stem.

 

 

    e.         What conclusions can you make from this table?

 

 

 

2.        Heather recently read about the following distribution which shows the number of pounds of each snack food eaten during the 2012 NCAA Basketball Championship game.

a.  Construct a pie chart for this data             b.  Indicate the degree of the central angle for each snack food

Potato chips                 12.3 million

Tortilla chips                8.4 million

Pretzels                                    7.8 million

Popcorn                       6.3 million

Snack Nuts                  2.5 million

 

 

3.   Attached to this exam are two sets of data, CU Women’s Softball stats for this season, and a recap of the weather in Portland. CHOOSE ONE of these sets of stats, and …

     a.   Make 3 observations of the data.

 

 

 

         b.   Pose two questions about the data that are critical to ask about any set of data.

 

 

 

4.   Jorge read that, in the Portland area, each month a household generates an average of 29 pounds of newspaper for recycling. The standard deviation is 2 pounds. Assume the data is normally distributed. What percentage of households…                    

     a.   Recycles between 27 and 31 pounds per month?

 

 

     b.   Recycles less than 33 pounds per month?

 

 

 

5.   Andrea obtained a math score of 510 on the SAT; the SAT scores had a mean of 435 and a standard deviation of 105. Her math score on the PSAT was 56; the PSAT scores had a mean of 42 and a standard deviation of 9.5.

a.  What is her z-score for the SAT?

 

 

b.  What is her z-score for the PSAT?

 

          

c.   Which of the two test scores from parts a and b indicates the stronger performance? Explain.

 

 

6.   Given the following results on the Stanford Achievement Test where the top row of numbers listed for each subject test shows the raw score for that subtest. The number in the second row of each column shows the national percentile.

 

 

Verbal

Math

Analytical

Raw Score

350

420

580

Percentile

65

85

92

a.         What percentage of the students scored above this student in Analytical skill?

 

b.         What percentage of the students scored below this student in Math?

7.   Since Summer is here, Rosa wants to put some color in her yard.  She bought 2 lilac, 2 rhododendron, and 1 rose bush. If an experiment consists of randomly choosing two of these bushes to plant in her yard, answer the following:

a.  List the sample space of this experiment.

 

 

 

b.  What is the probability that she will select 2 of the same bushes to put in her yard?

 

 

 

8.      Derrick is conducting an experiment consisting of tossing two ordinary dice and adding the two numbers. Determine the probability of him obtaining:

a.    A sum of  9                                b.   A sum less than 7                  c.  A sum greater than or equal to 10

 

 

 

9.      Going into the weekend, Michelle reported that the odds in favor of the weather being good enough to make her move a pleasant one are 7 to 9.

 

a.  What is the probability the weather will be good enough?

 

 

b.  What are the odds against the weather being good enough?

 

 

 

10.    Jerrilyn designed a multi-stage experiment using Starburst jelly beans with the following conditions: There are 1 orange, 8 yellow, 8 red and 2 purple jelly beans in a bowl. If an experiment consists of randomly selecting 2 jelly beans, and…

 

If they are INDEPENDENT events:

a.  What is the probability that both jelly beans will be yellow?

 

 

 

b.  What is the probability of choosing 1 red jelly bean and 1 orange jelly bean?

 

 

 

If they are DEPENDENT events:

c.  What is the probability that both jelly beans will be yellow?

 

 

 

d.  What is the probability of choosing 1 red jelly bean and 1 orange jelly bean?

 

11.    Jin decided to enter a raffle. Indicate which outcome (a or b) is more likely to occur: Assume there is one winning ticket in the box. Justify your answer.

a.      Obtaining a winning ticket by drawing once from a box of 15 tickets.

 

 

 

b.      Obtaining a winning ticket both times by drawing twice with replacement from a box of 5 tickets?

 

 

 

12.    Sandy is conducting an experiment consisting of spinning spinner 1 and then spinner 2.

 

 

Go to class (spinner 1)

Take a shower (spinner 2)

 
       
     
     

SPINNER 1                                         SPINNER 2

 

a.      What is the probability of her praying and then going to class?

 

 

 

b.      What is the probability she will jog and then take a shower?

 

 

 

13.    Alex decided to toss a coin three times and record the outcomes.

a.                Draw a probability tree illustrating all the possible

b.           What is the probability of at least one head when tossing three coins?

 

 

 

14.    Heinz bought a certain sweepstake ticket that has four categories of prizes with the following probabilities for winning.

 

              PRIZE                            PROBABILITY

            $500,000                               1/1,500,000

            $250,000                               1/500,000

            $100,000                               1/100,000

               $30,000                               1/18,000

 

a.      What is the expected value of buying this ticket? (Round to the nearest cent)

 

 

 

 

b.      If each ticket is $4.00, is this a fair contest? (Why/Why not?)

 

 

 

15.    When Abby was at work at Subway, she decided to try and figure out how many possible sandwiches are possible. If she knows that a person could have 5 different types of bread in 2 sizes, 10 kinds of meat, 4 kinds of cheese, 12 types of veggies, with 8 types of spread, how many different sandwiches are available if a person chooses one of each of the above options?

 

 

 

 

16.    Tyler discovered that the telephone company just instituted a new area code for certain districts in Oregon. He also found out that area codes and local numbers cannot begin with 0 or 1. How many different telephone numbers are possible? (Include the area code as part of the phone number.)

 

 

 

17.    In preparation for the upcoming Rose Festival in Portland, Julie decided to list in order of preference, her three favorite roses blooming at Washington Park. If she saw 45 different rose bushes, in how many ways can she choose and rank the top three?

 

 

 

18.    Heather just learned that our Math 110 class has been invited to attend a math conference at Disneyworld next fall. If all 20 Math 110 students attend:

a.  In how many ways can a luggage carrier, ticket holder and Mickey Mouse spotter be chosen from this group of students?

 

 

b.  In how many ways can 3of the students be chosen to represent us in a contest to not scream when riding “The Tower of Terror?”

 

 

c.  If a total of 63 people at the conference have entered the Tower of Terror contest, in how many

ways can the first 5 places come in?

CU Women’s Softball Overall Statistics

 

• Record: 18-9 • Home: 8-2 • Away: 2-5 • Neutral: 8-2 • CCC: 4-4 •

Player

avg

gp-gs

ab

r

h

2b

3b

hr

rbi

tb

slg%

bb

hbp

so

gdp

ob%

sf

sh

sb-att

po

a

e

fld%

1

.404

27-27

89

24

36

13

0

3

19

58

.652

13

0

8

0

.480

0

0

0-1

41

36

3

.963

2

.395

26-26

76

18

30

6

1

5

22

53

.697

10

3

6

1

.473

2

0

0-0

147

8

2

.987

3

.379

27-27

87

25

33

3

1

8

23

62

.713

7

1

11

0

.423

2

3

7-7

107

27

3

.978

4

.340

17-14

50

7

17

2

0

2

10

25

.500

5

1

3

0

.404

1

0

0-0

7

10

3

.850

5

.333

26-26

75

11

25

3

0

4

15

40

.533

13

2

10

0

.444

0

1

0-0

10

16

4

.867

6

.333

2-0

3

0

1

0

0

0

0

1

.333

0

0

0

0

.333

0

0

0-0

0

0

0

.000

7

.329

27-27

82

12

27

4

0

0

9

31

.378

5

0

7

1

.368

0

1

3-4

27

3

0

1.000

8

.321

26-25

81

17

26

3

0

0

8

29

.358

3

1

9

1

.353

0

3

3-3

29

1

3

.909

9

.302

27-27

86

13

26

2

0

3

14

37

.430

5

1

10

0

.344

1

2

2-3

44

1

0

1.000

10

.275

20-16

51

4

14

0

1

2

5

22

.431

4

2

5

2

.351

0

3

0-0

71

1

2

.973

11

.242

23-23

66

12

16

1

0

3

7

26

.394

2

0

6

0

.265

0

1

0-0

36

40

3

.962

12

.231

6-1

13

1

3

1

0

0

3

4

.308

0

0

3

0

.231

0

0

0-0

17

1

0

1.000

13

.200

18-12

5

1

1

0

0

0

0

1

.200

2

0

1

0

.429

0

0

1-1

6

25

4

.886

14

.000

7-1

6

0

0

0

0

0

0

0

.000

0

0

1

0

.000

0

0

0-0

0

0

0

.000

15

.000

17-0

5

7

0

0

0

0

0

0

.000

3

0

3

0

.375

0

0

4-6

1

0

0

1.000

16

.000

18-1

5

3

0

0

0

0

0

0

.000

1

0

1

0

.167

0

0

0-0

0

0

0

.000

17

.000

2-0

1

1

0

0

0

0

0

0

.000

0

0

1

0

.000

0

0

0-0

0

0

0

.000

18

.000

5-3

0

0

0

0

0

0

0

0

.000

0

0

0

0

.000

0

0

0-0

0

4

0

1.000

19

.000

17-14

0

0

0

0

0

0

0

0

.000

0

0

0

0

.000

0

0

0-0

3

9

1

.923

Totals

.327

27-27

781

156

255

38

3

30

135

389

.498

73

11

85

5

.389

6

14

20-25

546

182

28

.963

Opponents

.225

27-27

698

76

157

28

2

16

69

237

.340

78

7

163

1

.308

3

12

21-24

537

259

44

.948

 

LOB – Team (192), Opp (176). DPs turned – Team (4), Opp (9). IBB – Team (0), Opp (8). Picked off – BYRD 1.

 

 

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