Ch5 Evans BA1e

12 diet colas

5 cans of lemonade

3 cans of root beer

20 TOTAL

(a) PROBABILITY OF NEXT DRINK TO BE

diet colas 60%

cans of lemonade 25%

cans of root beer 15%

(b) Relative Frequency Definition of Probability

(a) (b)

Card 1 Card 2 SUM Value Frequency

1 1 2 2 1 Probability of the sum being 5

2 1 3 3 1

3 1 4 4 2

4 1 5 5 2

5 1 6 6 3 (c )

6 1 7 7 3

7 1 8 8 4 Probability of the sum being 2

8 1 9 9 4

9 1 10 10 5

10 1 11 11 5

2 2 4 12 5

3 2 5 13 4

4 2 6 14 4

5 2 7 15 3

6 2 8 16 3

7 2 9 17 2

8 2 10 18 2

9 2 11 19 1

10 2 12 20 1

3 3 6 TOTAL 55

4 3 7

5 3 8

6 3 9

7 3 10

8 3 11

9 3 12

10 3 13

4 4 8

5 4 9

6 4 10

7 4 11

8 4 12

9 4 13

10 4 14

5 5 10

6 5 11

7 5 12

8 5 13

9 5 14

10 5 15

6 6 12

7 6 13

8 6 14

9 6 15

10 6 16

SAMPLE SPACE

7 7 14

8 7 15

9 7 16

10 7 17

8 8 16

9 8 17

10 8 18

9 9 18

10 9 19

10 10 20

Probability of the sum being 5 3.64%

Probability of the sum being 2 1.82%

T T T 0.125

T T H 0.125

T H T 0.125

T H H 0.125

H T T 0.125

H T H 0.125

H H T 0.125

H H H 0.125

Sample Space

Pro

bab

ilities of e

ach o

utco

me

M Monster

RB Red Bull

RS Rockstar

(a) (b) Probability that RB will be the first choice

M RB RS

M RS RB

RB M RS

RB RS M (c ) Probability that two (independent) respondents will choose RB as their first

RS M RB

RS RB M

SAMPLE SPACE

=2/6

0.333333

Probability that two (independent) respondents will choose RB as their first

=2/6 * 2/6

0.111111

A Total card value is 5 or less

A^C Total card value is 6 or more

P(A) = 10.91%

P(B) = 89.09%

(a) A: exactly two heads P(A) = 3/8 0.375

(b) B: at most 1 heads P(B) = 4/8 0.5

(c ) C: at least 2 heads P(C ) = 4/8 0.5

(d) A and B are mutually exclusive

P(A or B) = 3/8 + 4/8 0.875

(e) A and C are not mutually exclusive.

P(A or C) = 3/8 + 4/8 - 3/8 0.5

(a) Event Name Description Probability

C1 Column 1 number 31.58%



O Odd Number 47.37%

E Even Number 47.37% Does not consider 0 or 00 even numbers

G Green Number 5.26%

F12 First 12 numbers 31.58%

S12 Second 12 numbers 31.58%

T12 Third 12 numbers 31.58%

(b) G or O 52.63%

O or F12 63.16% O and F12 15.79%

C1 or C3 63.16%

E and F12 15.79%

E or F12 63.16%

S12 and T12 63.16%

O or C2 63.16% O and C2 15.79%

Over the past 6 months

25 early

150 on time

45 late

30 cancelled

250 TOTAL

(a)

10% early

60% on time

18% late

12% cancelled

(b) The events are mutually exclusive

(c ) P(early or on time) 70%

PROBABILITIES

Of 100 graduates

50 only mutual funds

35 only stocks

15 both

(a) P(Own a mutual fund) 65%

P(Own a stock) 50%

(b) P(Neither stocks nor mutual funds) 0

(c ) P(Either stocks or mutual funds) 100

Census Education Data

Not a High

School Grad

High School

Graduate

Some College

No Degree

Associate's

Degree

Bachelor's

Degree

Total Persons 29,620,292 58,207,318 29,620,292 12,915,825 28,242,604

Age

25-34 4,683,126 12,553,926 7,792,092 3,423,798 8,382,402

35-44 5,335,440 15,117,080 8,136,546 4,134,966 8,136,546

45-54 4,427,540 10,932,618 6,062,324 2,894,930 5,960,150

55-64 4,562,275 8,301,115 3,338,250 1,157,260 2,893,150

65-74 5,165,297 6,505,772 2,466,474 768,539 1,787,300

75 and older 5,399,420 4,717,388 1,847,170 454,688 1,150,929

Gender

Male 14,168,672 26,607,448 14,086,296 5,683,944 14,086,296

Female 15,361,785 31,621,920 15,541,455 7,186,800 14,193,930

Race

White 23,647,714 49,181,442 24,953,416 11,171,006 24,373,104

Black 4,650,240 6,975,360 3,700,816 1,201,312 1,995,728

Other 1,279,740 1,977,780 1,047,060 550,676 1,915,732

Marital Status

Never Married 4,120,320 7,777,104 4,789,872 1,828,392 5,124,648

Married, spouse present 15,516,160 36,382,720 18,084,352 8,346,624 19,154,432

Married, spouse absent 1,847,880 2,368,024 1,184,012 465,392 670,712

Separated 1,188,090 1,667,010 842,715 336,165 405,240

Widowed 5,145,683 4,670,488 1,765,010 556,657 977,544

Divorced 2,968,680 7,003,040 3,806,000 1,674,640 2,340,690

Civilian Labor Force

Employed 11,668,755 36,228,706 20,448,104 9,890,659 22,115,069

Unemployed 1,057,310 1,783,636 809,072 317,193 455,103

Not in Labor Force 16,858,244 20,040,098 8,205,834 2,623,634 5,582,200

Advanced

Degree TOTAL

Not a High

School Grad

High School

Graduate

Some College

No Degree

Associate's

Degree

13,604,669 172,211,000 a) 10.49% 32.57% 18.38% 8.89%

2,439,948 b) A: has at least Associate's Degree

3,556,960 B: is at least a high school graduate

3,848,554

2,047,460 P(A) = 31.80%

1,179,618

625,196 P(B) = 82.80%

7,743,344 They are not mutually exclusive, since B includes A.

5,929,110

P(A or B) = P(B) = 82.80%

11,751,318

852,544

992,768

2,137,416

9,523,712

301,136

165,780

475,195

1,217,920

10,890,838 111,242,131

170,089

2,511,990

PROBABILITIES

Bachelor's

Degree

Advanced

Degree

19.88% 9.79%

PROBABILITIES

(a)

REGION Book DVD TOTAL

East 56 42 98 P(East) 20.76%

North 43 42 85 P(North) 18.01%

South 62 37 99 P(South) 20.97%

West 100 90 190 P(West) 40.25%

TOTAL 261 211 472

P(Book) P(DVD)

55.30% 44.70%

(b) P(Book | East) 57.14%

P(Book | North) 50.59%

P(Book | South) 62.63%

P(Book | EWest) 52.63%

a) P(unemployed and advanced degree)= 0.10%

b) P(unemployed advanced degree)= 0.10%

c) P(not a high school grad unemployed) = 0.61%

d) They are not independent, knowing the existence of one will affect the probability of the other.

Consumer Transportation Survey

Vehicle

Driven

Type Satisfacti

on with

vehicle

Gender

Truck Domestic Yes Male Count of Type Column Labels

Truck Domestic Yes Male Row Labels Car Mini Van

Truck Foreign No Male Female 16 8

Truck Domestic No Male Male 6 1

SUV Domestic Yes Male Grand Total 22 9

SUV Foreign Yes Male

SUV Domestic Yes Male

SUV Foreign Yes Male

SUV Domestic Yes Male a) 42%


SUV Foreign Yes Male b) 18%


SUV Foreign No Female c) 2%

SUV Foreign Yes Female

SUV Foreign Yes Female d) 10%


SUV Domestic No Female e) 27%

SUV Domestic No Female

SUV Domestic Yes Male f) 17%

Mini Van Domestic Yes Female

Mini Van Domestic No Female g) They are not independent. Men are more likely to drive SUVs. Women do not drive Trucks.


Mini Van Foreign Yes Female


Mini Van Domestic No Male




Car Domestic Yes Female

Car Domestic No Female


Car Foreign Yes Male

Car Domestic No Male





Car Foreign No Female

Car Foreign Yes Female











Car Foreign No Female

SUV Truck Grand Total

5 29

10 4 21

15 4 50

g) They are not independent. Men are more likely to drive SUVs. Women do not drive Trucks.

TP: Test shows pregnancy

NTP: Test does not show pregnancy

WP: Woman pregnant

NWP: Woman not pregnant

P(TP given NWP)= 0.02

P(NTP given WP)= 0.03

P(WP) = 0.70

P(WP given NTP) = P( WP and NTP) / P(NTP)

= [ P(NPT given WP) * P(WP) ] / P(NTP)

P(NTP) = P(NTP given WP) * P(WP) + P(NTP given NWP) *P(NWP)

0.03 * 0.70 + 0.98 * 0.30

31.50%

P(WP given NTP) = [ 0.03 * 0.70 ] / 0.315

6.67%

NOTE: THIS PROBLEM REQUIRES CONCEPTS OF BAYES'S THEOREM IN CHAPTER 18. IT WILL BE MODIFIED IN THE NEXT EDITION TO BETTER FIT THIS CHAPTER.

NOTE: THIS PROBLEM REQUIRES CONCEPTS OF BAYES'S THEOREM IN CHAPTER 18. IT WILL BE MODIFIED IN THE NEXT EDITION TO BETTER FIT THIS CHAPTER.

Drawing two 10s = 4 /40 * 3/39

0.77%

Drawing three 10s = 4 /40 * 3/39 * 2/38

0.04%

Two greens in a row = 2/38 * 2/38

0.28%

Two blacks in a row =18/38 * 18/38

22.44%

1

2

3

4

5

6

7

8

9

10

11

12

13

A B C D E G

e.g., P(S and F) = P(S given F)P(F)

P( Successful given Favorable) 48% P(Successful product and favorable test market)

P( Successful given Unfavorable) 12% P(Successful product and unfavorable test market)

P( Unsuccessful given Unfavorable) 28% P(Unuccessful product and favorable test market)

P( Unsuccessful given Favorable) 12% P(Unsuccessful product and unfavorable test market)

F: favorable 60%

UF: unfavorable 40%

S: successful 60%

US: unsuccessful 40%

1

2

3

4

5

6

7

8

9

10

11

12

13

H

28.8%

4.8%

7.2%

11.2%

Return Probability

-20% 0.10

0% 0.20

15% 0.40

30% 0.30

Expected Value 13%

Demand, x Probability, f(x) (x - Expected Value)^2

0 0.1 2.89

1 0.3 0.49

2 0.4 0.09

3 0.2 1.69

1.7 0.81

Expected Value Variance

0.90

Std Dev

7.84% 7.84% 7.84% 7.84% 7.84% 7.84% 7.84%

2 3 4 5 6 7 8

7.69% 2 0.45% 0.60% 0.60% 0.60% 0.60% 0.60% 0.60%

7.69% 3 0.60% 0.45% 0.60% 0.60% 0.60% 0.60% 0.60%

7.69% 4 0.60% 0.60% 0.45% 0.60% 0.60% 0.60% 0.60%

7.69% 5 0.60% 0.60% 0.60% 0.45% 0.60% 0.60% 0.60%

7.69% 6 0.60% 0.60% 0.60% 0.60% 0.45% 0.60% 0.60%

7.69% 7 0.60% 0.60% 0.60% 0.60% 0.60% 0.45% 0.60%

7.69% 8 0.60% 0.60% 0.60% 0.60% 0.60% 0.60% 0.45%

7.69% 9 0.60% 0.60% 0.60% 0.60% 0.60% 0.60% 0.60%

30.77% 10 2.41% 2.41% 2.41% 2.41% 2.41% 2.41% 2.41%

7.69% 11 0.60% 0.60% 0.60% 0.60% 0.60% 0.60% 0.60%

2 3 4 5 6 7 8

2 4 5 6 7 8 9 10

3 5 6 7 8 9 10 11

4 6 7 8 9 10 11 12

5 7 8 9 10 11 12 13

6 8 9 10 11 12 13 14

7 9 10 11 12 13 14 15

8 10 11 12 13 14 15 16

9 11 12 13 14 15 16 17

10 12 13 14 15 16 17 18

11 13 14 15 16 17 18 19

7.84% 31.37% 7.84% 2-CARD VALUE PROBABILITY Cumulative

9 10 11 4 0.45% 0.45%

0.60% 2.41% 0.60% 5 1.21% 1.66%

0.60% 2.41% 0.60% 6 1.66% 3.32%

0.60% 2.41% 0.60% 7 2.41% 5.73%

0.60% 2.41% 0.60% 8 2.87% 8.60%

0.60% 2.41% 0.60% 9 3.62% 12.22%

0.60% 2.41% 0.60% 10 4.07% 16.29%

0.60% 2.41% 0.60% 11 4.83% 21.12%

0.45% 2.41% 0.60% 12 8.90% 30.02%

2.41% 9.05% 2.41% 13 9.65% 39.67%

0.60% 2.41% 0.45% 14 8.90% 48.57%

15 8.45% 57.01%

9 10 11 16 7.69% (b) 64.71%

11 12 13 17 7.24% 71.95%

12 13 14 18 6.49% 78.43%

13 14 15 19 6.03% 84.46%

14 15 16 20 10.26% 94.72%

15 16 17 21 4.83% (a) 99.55%

16 17 18 22 0.45% 100.00%

17 18 19

18 19 20 P(16 or less) 64.71% ( c )

19 20 21

20 21 22 P(btw 12 & 16) 43.59%

P(btw 17 & 20) 30.02%

E[X] 14.62 ( d )

Variance 16.71

STD DEV 4.09

(X- E{X])^2

112.69

92.46

74.22

57.99

43.76

31.53

21.30

13.07

6.84

2.61

0.38

0.15

1.92

5.69

11.46

19.22

28.99

40.76

54.53

Consumer Transportation Survey

Vehicle

Driven

Type Satisfacti

on with

vehicle

Gender Age # of hours

per week in

vehicle

Miles

driven

per week

Number

of

Children

Average

number

of riders

Truck Domestic Yes Male 31 10 450 0 1

Truck Domestic Yes Male 29 5 370 1 1

Truck Foreign No Male 26 12 580 0 1

Truck Domestic No Male 18 6 300 0 1

SUV Domestic Yes Male 49 21 1000 0 1

SUV Foreign Yes Male 50 16 840 2 1







SUV Foreign No Female 39 6 280 1 1

SUV Foreign Yes Female 36 4 400 0 1

SUV Foreign Yes Female 33 3 420 0 1


SUV Domestic No Female 31 15 800 1 1

SUV Domestic No Female 29 4 300 1 1


Mini Van Domestic Yes Female 55 8 400 0 2

Mini Van Domestic No Female 43 10 700 2 3


Mini Van Foreign Yes Female 38 10 450 4 5


Mini Van Domestic No Male 35 5 350 2 2




Car Domestic Yes Female 21 4 150 0 1

Car Domestic No Female 62 5 175 0 2


Car Foreign Yes Male 60 5 150 0 1

Car Domestic No Male 58 10 600 0 1





Car Foreign No Female 42 5 400 2 3

Car Foreign Yes Female 41 5 350 2 2











Car Foreign No Female 19 5 500 0 2

Miles

from

work

Number

of

Children

COUNT Probability

Mass

Function

Cumulative

Distribution

Function

30 0 23 46.00% 46.00%

22 1 13 26.00% 72.00%

15 2 9 18.00% 90.00%

20 3 2 4.00% 94.00%

22 4 3 6.00% 100.00%

45

25 TOTAL 50

20

25 P(Fewer than two children) 72.00%

40

20 P(At least two children) 28.00%

15

17 P(Five or more children) 0.00%

20

25

35

50

20

15

0

0

15 P(

0

0

0

0

5

0

0

0

15

10

35

40

21

18

16

22

23

34

45

16

22

18

19

23

11

4

3

4

x f(x)

Months of Retention Probability (x-E[x])^2 E[x] Variance

1 15.00% 31.86 6.64 36.82

2 12.75% 21.57

3 10.84% 13.28

4 9.21% 6.99

5 7.83% 2.70

6 6.66% 0.42

7 5.66% 0.13

8 4.81% 1.84

9 4.09% 5.55

10 3.47% 11.26

11 2.95% 18.97

12 2.51% 28.68

13 2.13% 40.40

14 1.81% 54.11

15 1.54% 69.82

16 1.31% 87.53

17 1.11% 107.24

18 0.95% 128.95

19 0.80% 152.66

20 0.68% 178.38

21 0.58% 206.09

22 0.49% 235.80

23 0.42% 267.51

24 0.36% 301.22

25 0.30% 336.93

26 0.26% 374.64

27 0.22% 414.36

28 0.19% 456.07

29 0.16% 499.78

30 0.13% 545.49

31 0.11% 593.20

32 0.10% 642.91

33 0.08% 694.62

34 0.07% 748.33

35 0.06% 804.05

36 0.05% 861.76

37 0.04% 921.47

38 0.04% 983.18

39 0.03% 1,046.89

40 0.03% 1,112.60

41 0.02% 1,180.31

42 0.02% 1,250.03

43 0.02% 1,321.74

44 0.01% 1,395.45

45 0.01% 1,471.16

46 0.01% 1,548.87

47 0.01% 1,628.58

48 0.01% 1,710.29

Std Dev

6.07

Call Center Data

Male = 1

Female =

0

Yes = 1

No = 0

Yes = 1

No = 0

GenderStarting Age Prior Call Center ExperienceCollege DegreeLength of Service (years)

0 18 0 0 7.02

1 18 1 0 3.47

0 19 0 0 2.07

0 19 0 0 1.78

0 19 0 0 4.42

0 19 0 0 3.29

0 19 1 0 3.05

1 19 1 0 0.49

1 19 1 0 0.61

1 19 0 0 3.12

0 20 0 0 2.95

0 20 1 0 2.15

0 20 0 0 4.03

1 20 0 0 3.53

1 20 0 0 2.47

0 21 0 0 2.15

1 21 0 0 3.27

1 21 0 0 1.10

1 21 0 0 1.78

0 22 0 0 1.94

0 22 1 0 2.91

0 23 1 0 3.02

0 23 1 0 2.53

0 23 0 1 1.84

1 23 1 0 2.88

1 23 0 0 2.20

1 23 0 1 1.44

1 24 0 0 2.53

1 24 0 1 1.41

1 24 0 1 1.08

0 25 1 1 0.98

1 25 1 0 0.63

1 25 0 1 1.30

1 25 1 1 2.13

0 26 1 0 2.30

0 26 1 1 2.05

0 26 1 1 2.13

1 26 1 1 2.12

1 26 0 1 2.16

1 27 0 0 2.04

0 28 0 0 1.70

0 28 0 1 2.11

1 29 0 1 1.75

0 30 0 1 2.15

1 30 1 0 2.12

1 30 0 1 0.37

0 31 0 0 1.95

0 31 0 0 1.02

0 31 0 1 1.26

1 31 0 0 1.04

0 32 0 1 1.64

1 32 1 0 1.75

1 32 1 1 1.71

1 33 0 0 1.29

0 34 1 0 1.48

0 34 0 1 1.31

1 34 0 0 1.46

1 34 1 0 1.88

1 36 0 1 1.16

0 39 0 0 1.16

0 39 0 1 1.05

1 39 0 0 0.96

0 40 1 0 1.24

0 40 0 0 0.81

1 41 1 0 0.87

0 43 1 0 0.99

0 43 1 0 0.76

0 45 0 0 0.32

0 47 1 1 0.35

0 50 1 0 0.57

Binomial distribution

Experience Count

0 43

1 27

Probability of Experience 38.57%

n 25

p 0.05 p 0.05

Customers Contacted 25

Customers Generated 5 x f(x) F(x)

0 0.27739 0.27739

Probability of 25 potential contacts generating 5 customers 1 0.36499 0.64238

2 0.23052 0.87289

0.007164948 3 0.09302 0.96591

4 0.02693 0.99284

5 0.00595 0.99879

6 0.00104 0.99983

7 0.00015 0.99998

8 1.8E-05 1

9 1.8E-06 1

10 1.5E-07 1

11 1.1E-08 1

12 6.5E-10 1

13 3.4E-11 1

14 1.5E-12 1

15 6E-14 1

16 2E-15 1

17 5.5E-17 1

18 1.3E-18 1

19 2.5E-20 1

20 3.9E-22 1

21 4.9E-24 1

22 4.7E-26 1

23 3.2E-28 1

24 1.4E-30 1

25 3E-33 1

p 50% success

Total Weeks 52

Success Weeks 33

Probability of 33 weeks of success by chance

1.70%

p 4%

Hotel Rooms 300

Cancellations 20 (300 - 280)

Probability of at least 280 rooms will be occupied

98.99%

Normal Approximation

Mean 288.00

S.D. 3.39

For 280 rooms, z score

z (2.36)

Probability 99.08%

p 0.10

Number of Calls 78

Number of Successes 4

Probability of up to 4 successes

9.94%

Probability of 5 or more successes

90.06%

1

2

3

4

5

6

7

8

9

10

11

A B C D E

Average 6 customers per day

Customers per

day Probability

0 0.25%

1 1.49%

2 4.46%

3 8.92%

4 13.39%

at least 5 71.49%

Empirical Theoretical

Number Frequency Probability Probability

0 5 7.35% 7.52%

1 16 23.53% 19.45%

2 19 27.94% 25.17%

3 13 19.12% 21.72%

4 3 4.41% 14.05%

5 5 7.35% 7.27%

6 4 5.88% 3.14%

7 2 2.94% 1.16%

8 1 1.47% 0.38%

TOTAL 68

2.59 Expected Value0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

1 2 3

3 4 5 6 7 8 9

Empirical Probability

Theoretical Probability

Using formulas

a. P(x<8) 60% 0.60

b. P(x>7) 40% 0.40

c. P(6<x<10) 80% 0.80

d. P(8<x<11) 30% 0.30

a 20 minutes

b 60 minutes

a. Mean 40.00 minutes

Variance 133.33

b. 12.50%

c. 50.00%

Using formula

a 10 Minimum a 10

b 20 Maximum b = ? 20 (18-10) = .8x and solve for x

P(in 18 days) 0.8 P(in 18 days) 0.80

(18-10) = .8x and solve for x

Mean 30 mpg

S.D. 1.5 mpg

a. P(X<28) 9.12%

b. P(X<32) 90.88%

P(28<X<32) 81.76%

c. P(X<33) 97.72%

P(X>33) 2.28%

d. P(X<31) 74.75%

e. Upper tail 5%

Lower cum 95%

mpg 32.47 upper 5%

Mean 580

S.D. 25

a. P(X<550) 11.51%

b. P(X<600) 78.81%

P(X<560) 21.19%

P(560<X<600) 57.63%

c. P(X<620) 94.52%

P(X>620) 5.48%

d. P(X<700) 99.9999%

P(X>700) 0.0001%

e. 500 (3.20)

Z-scores 600 0.80

700 4.80

Mean 2000 ml

S.D. 20 ml

a. P(X<2060) 99.87%

Overfill 0.13%

b. P(X<1970) 6.68%

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

A B C D E F G H I J

Mean 1.98 cm

S.D. 0.10 cm

a. P(X<2.04) 72.57%

P(X<1.96) 42.07%

Meet the specs 30.50%

b.

Mean 2.00 cm

S.D. 0.10 cm

P(X<2.04) 65.54%

P(X<1.96) 34.46%

Meet the specs 31.08%

c. Using formula lower limit 2.04

upper limit 1.96

Mean 2.00 cm Mean 2.00 cm

S.D. 0.017 cm S.D. 0.0172 cm

Z=

P(X<2.04) 99.07% P(X<2.04) -2.33

P(X<1.96) 0.93% P(X<1.96) 2.33

Meet the specs 98.14% Meet the specs 98.00%

Mean 20.00$

S.D. 4.00$

P(at most $15) 10.56%

P(at least $15) 89.44%

100 customers

Mean 20.00$

S.D. 0.40$

p(1 customer spends at least $15) 89.44%

P(at least 40 customers) 100.00%

Mean 2750

Lambda 0.0004

P(X>3000) 33.59%

Mean 20 minutes

Lambda 0.05

a. P(X<30) 77.69%

P(X>30) 22.31%

b. P(X<20) 63.21%

PROBABILITY OF NEXT DRINK TO BE OUTCOME

diet colas 0.60 - to less than 0.60 diet colas

cans of lemonade 0.25 0.60 to less than 0.85 cans of lemonade

cans of root beer 0.15 0.85 to less than 1.00 cans of root beer

Interval

OUTCOME Random Number OUTCOME

0.2479 diet colas

cans of lemonade 0.8383 cans of lemonade

cans of root beer 0.6292 cans of lemonade

0.6219 cans of lemonade

0.4159 diet colas

0.8737 cans of root beer




0.3619 diet colas

SAMPLE SPACE

Value Frequency Probability OUTCOME

2 1 0.0182 - to less than 0.0182 2

3 1 0.0182 0.0182 to less than 0.0364 3

4 2 0.0364 0.0364 to less than 0.0727 4

5 2 0.0364 0.0727 to less than 0.1091 5

6 3 0.0545 0.1091 to less than 0.1636 6

7 3 0.0545 0.1636 to less than 0.2182 7

8 4 0.0727 0.2182 to less than 0.2909 8

9 4 0.0727 0.2909 to less than 0.3636 9

10 5 0.0909 0.3636 to less than 0.4545 10

11 5 0.0909 0.4545 to less than 0.5455 11

12 5 0.0909 0.5455 to less than 0.6364 12

13 4 0.0727 0.6364 to less than 0.7091 13

14 4 0.0727 0.7091 to less than 0.7818 14

15 3 0.0545 0.7818 to less than 0.8364 15

16 3 0.0545 0.8364 to less than 0.8909 16

17 2 0.0364 0.8909 to less than 0.9273 17

18 2 0.0364 0.9273 to less than 0.9636 18

19 1 0.0182 0.9636 to less than 0.9818 19

20 1 0.0182 0.9818 to less than 1.0000 20

TOTAL 55

Interval

OUTCOME Random Number OUTCOME

0.4002 10

0.0985 5

0.1781 7

0.7549 14

0.3978 10

0.9806 19

0.3833 10

0.8754 16

0.9646 19

0.5565 12

a 20 minutes

b 60 minutes

RAND NUMBER MEAN 40.70

1 0.9937 59.75 S.D. 12.19

2 0.6465 45.86

3 0.5246 40.98

4 0.7414 49.65

5 0.0290 21.16

6 0.8123 52.49

7 0.6222 44.89

8 0.9325 57.30

9 0.6910 47.64

10 0.1408 25.63

11 0.8166 52.66

12 0.3392 33.57

13 0.6599 46.39

14 0.9174 56.70

15 0.6930 47.72

16 0.4772 39.09

17 0.3777 35.11

18 0.3569 34.28

19 0.9044 56.17

20 0.0175 20.70

21 0.4548 38.19

22 0.2311 29.25

23 0.1528 26.11

24 0.3727 34.91

25 0.0320 21.28

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

A B C D E F G H I

8 Min 2 COUNT FREQ

6 Max 13 2 2

6 3 8

10 4 15

7 5 19

5 6 10

5 7 13

8 8 13

7 9 6

10 10 10

4 11 3

6 12 0

5 13 1

4

3 75% of the days there will be at least 5 customers

6

7

5

9

4

8

6

4

9

5

11

7

4

4

5

3

8

8

8

10

3

13

4

5

9

5

4

7

8

8

11

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

A B C D E F G H I

5

3

4

10

8

5

7

8

9

10

3

8

9

2

5

6

8

7

5

4

4

3

10

5

5

10

7

4

4

8

10

6

5

7

6

6

9

10

4

5

3

7

10

5

7

4

93

94

95

96

97

98

99

100

A B C D E F G H I

5

3

7

2

11

7

6

5

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

J K

of the days there will be at least 5 customers

NOTE: AS A SAMPLING EXPERIMENT, THE RESULTS WILL VARY SLIGHTLY FOR EACH STUDENT

Equity Multiplier 4.00

3.80% 1.50 MEAN

0.40% 0.20 S.D.

Net Profit

Margin

Total Asset

Turnover ROE

3.97% 1.90 0.30 min 0.12

3.01% 1.18 0.14 max 0.37

3.66% 1.65 0.24

3.39% 1.60 0.22

3.69% 1.29 0.19

3.71% 1.83 0.27

3.19% 1.46 0.19

4.19% 1.72 0.29

3.94% 1.34 0.21

4.05% 1.57 0.25

4.15% 1.66 0.28

4.27% 1.53 0.26

4.07% 1.46 0.24

3.64% 1.50 0.22

3.73% 1.48 0.22

3.92% 1.33 0.21

3.50% 1.22 0.17

3.40% 1.24 0.17

3.67% 1.29 0.19

4.01% 1.35 0.22

4.16% 1.17 0.19

3.46% 1.60 0.22

3.71% 1.43 0.21

3.90% 1.46 0.23

3.66% 1.53 0.22

4.64% 1.74 0.32

3.21% 1.49 0.19

3.37% 1.36 0.18

4.41% 1.88 0.33

3.82% 1.48 0.23

4.05% 1.39 0.23

3.83% 1.62 0.25

3.01% 1.62 0.19

4.18% 1.31 0.22

4.12% 1.63 0.27

4.05% 1.49 0.24

3.56% 1.07 0.15

3.74% 1.15 0.17

3.38% 1.62 0.22

4.11% 1.46 0.24

3.97% 1.25 0.20

4.19% 1.61 0.27

3.91% 1.42 0.22

3.72% 1.29 0.19

3.83% 1.23 0.19

3.68% 1.55 0.23

4.31% 1.57 0.27

3.82% 1.58 0.24

3.25% 1.89 0.25

3.87% 1.46 0.23

3.39% 1.18 0.16

3.35% 1.76 0.24

4.07% 1.88 0.31

3.04% 1.39 0.17

3.87% 1.47 0.23

3.46% 1.76 0.24

3.65% 1.64 0.24

4.15% 1.54 0.26

4.54% 1.43 0.26

4.36% 1.42 0.25

4.32% 1.27 0.22

3.46% 1.42 0.20

3.23% 1.34 0.17

3.17% 1.53 0.19

4.00% 1.54 0.25

3.05% 1.32 0.16

2.85% 1.61 0.18

3.64% 1.56 0.23

4.34% 1.28 0.22

4.59% 1.22 0.22

3.71% 1.45 0.22

3.21% 1.58 0.20

3.83% 1.60 0.24

4.09% 1.58 0.26

3.51% 1.78 0.25

3.81% 1.55 0.24

3.52% 1.63 0.23

3.78% 1.43 0.22

3.87% 1.39 0.22

3.99% 1.30 0.21

3.95% 1.66 0.26

4.24% 1.46 0.25

3.10% 1.54 0.19

3.15% 1.24 0.16

4.89% 1.57 0.31

4.26% 1.66 0.28

3.69% 1.70 0.25

3.88% 1.50 0.23

3.52% 1.47 0.21

3.94% 1.54 0.24

4.39% 1.51 0.26

4.54% 1.23 0.22

3.41% 1.42 0.19

4.11% 1.72 0.28

4.08% 1.29 0.21

4.26% 1.57 0.27

4.57% 1.77 0.32

3.69% 1.80 0.27

3.83% 1.68 0.26

4.13% 1.37 0.23

3.25% 1.66 0.22

3.77% 1.71 0.26

4.24% 1.50 0.25

4.42% 1.79 0.32

3.97% 1.82 0.29

4.09% 1.38 0.23

3.86% 1.33 0.21

3.95% 1.34 0.21

3.58% 1.23 0.18

3.52% 1.80 0.25

3.85% 1.48 0.23

3.26% 1.40 0.18

3.22% 1.13 0.15

4.39% 1.62 0.28

3.37% 1.36 0.18

3.62% 1.65 0.24

4.35% 1.55 0.27

4.11% 1.93 0.32

4.78% 1.45 0.28

3.72% 1.67 0.25

3.60% 1.27 0.18

4.31% 1.54 0.27

3.59% 1.76 0.25

3.88% 1.60 0.25

3.47% 1.55 0.22

4.45% 1.30 0.23

4.09% 1.60 0.26

4.04% 1.32 0.21

3.89% 1.37 0.21

3.02% 1.00 0.12

3.05% 1.26 0.15

3.51% 1.32 0.19

3.65% 1.29 0.19

4.02% 1.39 0.22

3.56% 1.52 0.22

3.52% 1.47 0.21

4.04% 1.71 0.28

4.54% 1.59 0.29

3.44% 1.52 0.21

3.33% 1.22 0.16

4.45% 1.69 0.30

4.28% 1.43 0.24

3.73% 1.77 0.26

4.23% 1.40 0.24

4.65% 1.29 0.24

3.72% 1.32 0.20

2.88% 1.18 0.14

4.30% 1.05 0.18

4.35% 1.40 0.24

4.32% 1.90 0.33

3.39% 1.50 0.20

4.19% 1.41 0.24

3.32% 1.68 0.22

3.94% 1.77 0.28

3.59% 1.54 0.22

3.68% 1.46 0.21

4.22% 1.58 0.27

3.06% 1.61 0.20

3.59% 1.25 0.18

3.46% 1.33 0.18

3.54% 1.57 0.22

3.10% 1.53 0.19

3.75% 1.66 0.25

3.52% 1.32 0.19

3.53% 1.34 0.19

3.96% 1.66 0.26

3.55% 1.46 0.21

4.26% 1.39 0.24

3.93% 1.62 0.26

3.76% 1.71 0.26

4.94% 1.40 0.28

3.41% 1.38 0.19

3.83% 1.48 0.23

4.10% 1.90 0.31

3.81% 1.25 0.19

3.95% 1.86 0.29

4.84% 1.29 0.25

3.07% 1.44 0.18

3.25% 1.34 0.17

3.60% 1.57 0.23

2.58% 1.69 0.17

3.79% 1.78 0.27

4.02% 1.31 0.21

4.43% 1.71 0.30

3.89% 1.29 0.20

3.34% 1.44 0.19

3.33% 1.67 0.22

4.20% 1.53 0.26

3.56% 1.53 0.22

4.01% 1.41 0.23

4.06% 1.34 0.22

4.07% 1.33 0.22

4.07% 1.73 0.28

3.62% 1.22 0.18

3.40% 1.69 0.23

3.79% 1.50 0.23

3.55% 1.36 0.19

4.02% 1.32 0.21

3.09% 1.43 0.18

3.48% 1.70 0.24

4.12% 1.65 0.27

3.98% 1.10 0.17

4.10% 1.40 0.23

3.88% 1.89 0.29

4.03% 1.54 0.25

3.76% 1.50 0.23

4.13% 1.39 0.23

4.19% 1.08 0.18

4.36% 1.55 0.27

3.96% 1.21 0.19

3.15% 1.56 0.20

3.54% 1.81 0.26

3.72% 1.48 0.22

3.62% 1.32 0.19

3.65% 1.78 0.26

4.01% 1.06 0.17

3.47% 1.25 0.17

3.84% 1.31 0.20

4.57% 1.26 0.23

3.56% 1.55 0.22

3.86% 1.35 0.21

4.66% 1.88 0.35

4.26% 1.74 0.30

3.67% 1.45 0.21

3.11% 1.49 0.19

3.62% 1.61 0.23

4.48% 1.29 0.23

4.63% 1.60 0.30

3.91% 1.38 0.22

4.05% 1.83 0.30

3.76% 1.29 0.19

3.66% 1.55 0.23

4.31% 1.48 0.25

4.01% 1.54 0.25

3.68% 1.90 0.28

3.22% 1.09 0.14

3.81% 1.52 0.23

3.72% 1.50 0.22

4.12% 1.39 0.23

3.22% 1.48 0.19

3.50% 1.67 0.23

3.95% 1.68 0.27

3.80% 1.23 0.19

4.08% 1.32 0.22

3.86% 1.72 0.27

3.34% 1.26 0.17

3.93% 1.56 0.25

5.12% 1.81 0.37

3.63% 1.39 0.20

3.65% 1.40 0.20

NOTE: AS A SAMPLING EXPERIMENT, THE RESULTS WILL VARY SLIGHTLY FOR EACH STUDENT

Range Cumulative Frequency

0.12 0

0.13 1 1

0.14 3 2

0.15 5 2

0.16 8 3

0.17 15 7

0.18 27 12

0.19 45 18

0.20 66 21

0.21 81 15

0.22 107 26

0.23 141 34

0.24 159 18

0.25 182 23

0.26 198 16

0.27 212 14

0.28 224 12

0.29 231 7

0.30 236 5

0.31 241 5

0.32 244 3

0.33 247 3

0.34 248 1

0.35 248 0

0.36 249 1

0

5

10

15

20

25

30

35

40

0.1

2

0.1

3

0.1

4

0.1

5

0.1

6

0.1

7

0.1

8

0.1

9

0.2

0

0.2

1

0.2

2

0.2

3

0.2

4

0.2

5

0.2

6

0.2

7

0.2

8

0.2

9

0.3

0

Frequency

0.3

0

0.3

1

0.3

2

0.3

3

0.3

4

0.3

5

0.3

6

Scenario 1 2 3 4 5 6 7 8

1 3.38$ 3.60$ 3.72$ 3.08$ 3.84$ 3.55$ 3.77$ 3.84$

2 3.11$ 3.04$ 3.18$ 3.82$ 3.53$ 3.65$ 3.52$ 3.79$

3 3.59$ 3.10$ 3.63$ 3.36$ 3.27$ 3.01$ 3.55$ 3.89$

4 4.12$ 3.05$ 3.78$ 3.19$ 3.56$ 3.71$ 3.68$ 3.48$

5 3.68$ 3.27$ 3.53$ 3.53$ 3.28$ 3.26$ 3.69$ 3.50$

6 3.20$ 3.42$ 3.12$ 3.67$ 3.68$ 2.85$ 3.92$ 3.86$

7 3.37$ 3.71$ 3.28$ 3.65$ 3.90$ 3.64$ 3.77$ 3.79$

8 3.44$ 3.83$ 3.31$ 3.60$ 3.71$ 3.33$ 3.76$ 3.43$

9 3.72$ 3.65$ 3.54$ 3.41$ 3.64$ 3.94$ 3.32$ 3.61$

10 3.28$ 3.40$ 3.18$ 3.60$ 3.40$ 3.31$ 3.63$ 3.49$

11 3.57$ 3.63$ 3.01$ 3.67$ 3.32$ 3.36$ 3.64$ 3.68$

12 3.49$ 3.66$ 3.72$ 3.27$ 3.17$ 2.96$ 3.54$ 3.61$

13 3.73$ 3.09$ 3.52$ 3.74$ 3.20$ 3.76$ 3.37$ 4.20$

14 3.40$ 3.02$ 3.37$ 3.56$ 3.59$ 3.50$ 3.44$ 3.65$

15 3.05$ 3.42$ 3.27$ 3.65$ 3.38$ 3.80$ 4.01$ 2.92$

16 3.20$ 3.75$ 3.54$ 3.86$ 3.43$ 3.51$ 3.62$ 3.44$

17 3.58$ 3.28$ 3.86$ 3.53$ 3.35$ 3.65$ 3.37$ 3.63$

18 3.48$ 3.75$ 3.45$ 3.12$ 3.54$ 3.41$ 2.91$ 3.49$

19 3.41$ 3.41$ 4.11$ 3.32$ 3.64$ 3.79$ 3.55$ 3.55$

20 3.52$ 3.63$ 3.78$ 3.94$ 3.39$ 3.84$ 4.05$ 3.47$

21 3.95$ 3.66$ 3.19$ 3.33$ 3.97$ 3.26$ 3.93$ 3.17$

22 3.49$ 3.62$ 3.71$ 3.13$ 3.41$ 3.51$ 3.40$ 3.59$

23 3.62$ 3.54$ 3.65$ 3.65$ 3.43$ 3.45$ 3.61$ 3.00$

24 3.57$ 3.79$ 3.79$ 2.87$ 2.97$ 3.74$ 3.98$ 3.45$

25 3.29$ 2.93$ 3.98$ 3.69$ 3.23$ 3.88$ 3.85$ 3.66$

9 10 MIN BID MEAN 3.50$ million

3.14$ 3.85$ 3.08$ SD 0.25$ million

2.89$ 3.74$ 2.89$

3.19$ 3.86$ 3.01$

3.71$ 3.14$ 3.05$

3.90$ 3.09$ 3.09$

3.32$ 3.45$ 2.85$

2.90$ 3.77$ 2.90$

3.47$ 3.36$ 3.31$

3.26$ 3.74$ 3.26$

3.48$ 3.64$ 3.18$

3.72$ 3.43$ 3.01$

3.51$ 4.13$ 2.96$

3.55$ 3.80$ 3.09$

3.34$ 3.36$ 3.02$

3.03$ 3.81$ 2.92$

3.35$ 3.20$ 3.20$

3.70$ 3.33$ 3.28$

3.31$ 3.82$ 2.91$

3.55$ 3.13$ 3.13$

3.39$ 3.96$ 3.39$

3.50$ 3.81$ 3.17$

3.82$ 3.34$ 3.13$

3.58$ 3.71$ 3.00$

3.26$ 3.58$ 2.87$

3.37$ 3.14$ 2.93$

3.07$ EXPECTED VALUE

Computer Repair Times

Sample Repair Time (Days)

1 182 153 174 95 376 157 88 299 10

10 1411 1712 1213 13

14 12

15 11

16 14

17 13

18 16

19 13

20 15

21 16

22 12

23 34

24 29

25 13

26 19

27 12

28 15

29 16

30 14

31 15

32 7

33 40

34 16

35 11

36 11

37 10

38 13

39 14

40 9

41 18

42 8

43 13

44 8

45 10

46 13

47 16

48 9

49 9

50 12

51 16

52 9

53 15

54 17

55 38

56 11

57 15

58 16

59 10

60 9

61 25

62 15

63 7

64 11

65 19

66 13

67 12

68 20

69 12

70 13

71 11

72 8

73 14

74 10

75 12

76 15

77 17

78 10

79 13

80 18

81 26

82 14

83 15

84 12

85 15

86 9

87 10

88 21

89 11

90 36

91 8

92 20

93 14

94 18

95 19

96 14

97 12

98 16

99 17

100 12

101 10

102 10

103 15

104 23

105 13

106 19

107 19

108 12

109 13

110 12

111 16

112 12

113 14

114 11

115 14

116 7

117 16

118 12

119 16

120 10

121 12

122 36

123 9

124 9

125 22

126 16

127 12

128 17

129 9

130 25

131 14

132 13

133 13

134 8

135 14

136 8

137 17

138 13

139 12

140 8

141 12

142 17

143 22

144 19

145 10

146 19

147 10

148 17

149 13

150 9

151 13

152 9

153 11

154 12

155 17

156 15

157 15

158 27

159 17

160 10

161 20

162 15

163 12

164 15

165 23

166 17

167 8

168 17

169 10

170 20

171 16

172 12

173 11

174 22

175 11

176 14

177 17

178 18

179 11

180 21

181 15

182 14

183 16

184 10

185 19

186 14

187 20

188 27

189 20

190 15

191 20

192 11

193 14

194 13

195 26

196 9

197 8

198 15

199 16

200 21

201 14

202 15

203 15

204 14

205 15

206 15

207 16

208 5

209 11

210 14

211 8

212 21

213 10

214 18

215 13

216 16

217 11

218 11

219 10

220 18

221 11

222 18

223 23

224 22

225 19

226 9

227 11

228 10

229 6

230 39

231 14

232 10

233 11

234 7

235 13

236 17

237 8

238 25

239 20

240 13

241 21

242 7

243 12

244 16

245 23

246 18

247 31

248 6

249 17

250 13

ONE EXAMPLE:Chi-Square

Ch5 Evans BA1e

Documents