Electronic Keno Project 3 Overview and Rationale This assignment is designed to provide you with hands-on experience in using discrete and continuous probability distributions. In this assignment you will use technology to generate random samples and explore the samples’ relationship with the underlying population. Finally, you will have an opportunity to apply the Central Limit Theorem to inferential statistics. Course Outcomes This assignment is directly linked to the following key learning outcomes from the course syllabus: CO2: Create distributions and graphical representation based on given data and identify which distribution models best fit the data CO3: Apply the theory of probability to calculate events’ likelihoods, understanding the differences between experimental and theoretical probabilities (the Law of Large Numbers), and calculate posterior probabilities by using the Bayes’ Law with emphasis on applications CO7: Interpret meaningful relationships and patterns in the data in relation to a given business question Assignment Summary Read the scenario below and follow the instructions in the project description below (Parts 1 and 2) to analyze the data presented in the Excel workbook (Module 3 Project_Keno_v1.xlsx). Complete all parts in the designated Excel workbook. Submit both the report and the Excel workbook. The Excel workbook contains all statistical work. The report should include all your findings along with important analysis. Project Description The game of Keno: keno is an ancient Chinese game that has become popular in recent years. In one electronic version of this game, a player selects 20 numbers from the set of numbers 1 through 100. The computer then randomly draws another set of 20 numbers from the set 1 through 100, and the player is rewarded according to how many of his selected numbers have been matched by the 20 numbers drawn by the computer. Part 1 Let X be the number of matches between a player’s 20 selected numbers and the 20 numbers drawn by the computer. Then X may range from 0 (no match) to 20 (all match) and follows a hyper-geometric probability distribution. Complete all of the following steps (a – j) in worksheet Part 1 of the Excel workbook provided. All cells should contain formulas. a. Construct a tabular probability distribution for X in column E of the worksheet. b. Construct a tabular cumulative probability distribution for X in column F of the worksheet. c. Create a graphical probability distribution for X. d. Create a graphical cumulative probability distribution for X. e. Calculate the theoretical expected value (mean), the theoretical variance, and the theoretical standard deviation of X in the spaces provided for those quantities. Interpret those values in your Word report f. In column M of the worksheet, use the Excel function “=RAND()” to generate 1000 random values according to the standard uniform ...

1. Electronic Keno
Project 3
Overview and Rationale
This assignment is designed to provide you with hands-on
experience in using discrete and
continuous probability distributions. In this assignment you will
use technology to
generate random samples and explore the samples’ relationship
with the underlying
population. Finally, you will have an opportunity to apply the
Central Limit Theorem to
inferential statistics.
Course Outcomes
This assignment is directly linked to the following key learning
outcomes from the course
syllabus:
CO2: Create distributions and graphical representation based on
given data and identify
which distribution models best fit the data
CO3: Apply the theory of probability to calculate events’
likelihoods, understanding the
differences between experimental and theoretical probabilities

2. (the Law of Large
Numbers), and calculate posterior probabilities by using the
Bayes’ Law with emphasis on
applications
CO7: Interpret meaningful relationships and patterns in the data
in relation to a given
business question
Assignment Summary
Read the scenario below and follow the instructions in the
project description below (Parts
1 and 2) to analyze the data presented in the Excel workbook
(Module 3
Project_Keno_v1.xlsx). Complete all parts in the designated
Excel workbook. Submit both
the report and the Excel workbook. The Excel workbook
contains all statistical work. The
report should include all your findings along with important
analysis.
Project Description
The game of Keno: keno is an ancient Chinese game that has
become popular in recent
years. In one electronic version of this game, a player selects 20
numbers from the set of
numbers 1 through 100. The computer then randomly draws
another set of 20 numbers

3. from the set 1 through 100, and the player is rewarded
according to how many of his
selected numbers have been matched by the 20 numbers drawn
by the computer.
Part 1
Let X be the number of matches between a player’s 20 selected
numbers and the 20
numbers drawn by the computer. Then X may range from 0 (no
match) to 20 (all match)
and follows a hyper-geometric probability distribution.
Complete all of the following steps (a – j) in worksheet Part 1
of the Excel workbook
provided. All cells should contain formulas.
a. Construct a tabular probability distribution for X in column E
of the worksheet.
b. Construct a tabular cumulative probability distribution for X
in column F of the
worksheet.
c. Create a graphical probability distribution for X.
d. Create a graphical cumulative probability distribution for X.
e. Calculate the theoretical expected value (mean), the
theoretical variance, and the
theoretical standard deviation of X in the spaces provided for
those quantities. Interpret
those values in your Word report
f. In column M of the worksheet, use the Excel function
“=RAND()” to generate 1000
random values according to the standard uniform probability
distribution.

4. g. In column N of the worksheet, use the Excel “=VLOOKUP()”
function along with the
available tabular cumulative distribution of part (b) to randomly
generate 1000 values
of X according to the described Hyper-geometric probability
distribution.
h. Calculate the experimental (simulated) expected value
(mean), the experimental
variance, and the experimental standard deviation of X in the
spaces provided for those
quantities.
i. Complete the table in columns Q, R, and S of the worksheet.
In completing this table,
you should calculate the experimental means successively after
n = 20, 40, 60, 80, 100,
200, 300, 400, 500, 600, 700, 800, 900, and 1000 simulations. It
is natural that the
calculated experimental means are refreshed after each new
operation in the
worksheet. For the Theoretical mean of X in column S, use the
fixed value of the
theoretical mean calculated in part (e).
j. Create a line plot of the Experimental mean values versus the
number of simulations
(n). Add the horizontal line plot displaying the theoretical mean
of X. Use the f9 function

5. of your keyboard (Mac: fn+f9) to run several simulations of the
successive experimental
means. Interpret your observation in the context of the Law of
Large Numbers (as the
number of simulations become larger, the experimental values
of the means approach
to their theoretical value).
Part 2
Complete all of the following steps (a – i) in worksheet Part 2
of the Excel workbook
provided.
a. A normal population is given in column E of the worksheet.
Calculate the mean, the
variance, and the standard deviation of this population in the
designated cells.
b. Construct a Relative Frequency Histogram of the given
population. Discuss the shape of
the distribution.
c. Using the random sampling method described in the
Instructor Perspective (or
otherwise; e.g., using the Data Analysis ToolPak), randomly
draw 30 samples with each
sample consisting of 30 measurements from this population.
These samples will occupy
columns N through AQ.
d. For each sample, calculate the sample mean, the sample
variance, and the sample
standard deviation in the designated cells.
e. Calculate the average of 30 sample means, the average of 30

6. sample variances, and the
average of 30 sample standard deviations in the designated cells
K2, K3, and K4
respectively.
f. Compare your results of part (e) above with those obtained
for the population in part
(a). Discuss similarities and contrasts in the context of the
Central Limit Theorem.
g. Construct a relative frequency histogram for the 30 sample
means obtained from part
(e) above. Comment on the shape of the distribution of the
sample means.
h. Summarize your findings of this experiment in your Word
report.
Format & Guidelines
The report should follow the following format:
(i) Introduction
(ii) Analysis
(iii) Conclusion
And be 800-900 words and be presented in the APA format.
The Excel spreadsheet must be completed as outlined in the
assignment above.

7. Rubric
Category Above Standard Meets Standards Approaching
Standards Below Standards Not Evident
Excel (or R):
Problem
Modeling &
Set-up
ALY6010_CO3
Thoroughly and
concisely modeled the
problem in Excel (or R)
for each method
Accurately modeled the
problem in Excel (or R)
for each method
Satisfactorily modeled
the problem in Excel (or
R) for each method.
Partially modeled the
problem in Excel (or R)
for each method, but
there are some gaps in
the problem modeling

8. and setup
Did not submit or
incompletely modeled
the problem in Excel (or
R)
Excel (or R):
Problem
Solution
&
Accuracy
ALY6010_CO3
Thoroughly and
efficiently obtained
correct and accurate
solutions in Excel (or R)
by using the appropriate
analytic tools of the
software
Thoroughly obtained
accurate solutions in
Excel (or R) by using the

9. appropriate analytic
tools of the software
Satisfactorily obtained
correct solutions in
Excel (or R) by using the
appropriate analytic
tools of the software
Partially obtained
accurate solutions in
Excel (or R) by using the
appropriate analytic
tools of the software
Did not submit or did
not obtain accurate
solutions in Excel (or R)
using the appropriate
analytic tools of the
software
Word/Report:
Problem
Description &

10. Introduction
ALY6010_CO5
Thoroughly provided a
summary of the problem
descriptions and
introduced the problem
using rich and significant
ideas
Thoroughly provided a
summary of the problem
descriptions and
problem introduction
Satisfactorily provided a
summary of the problem
descriptions and
problem introduction
Partially provided a
summary of the problem
descriptions and problem
introduction

11. Did not submit or did
not provide a summary
of the problem
descriptions and
problem introduction
Word/Report:
Description of
Problem
Analysis
ALY6010_CO5
Thoroughly and
accurately described the
analytic concepts and
theories used in
analyzing the problem
Accurately described the
analytic concepts and
theories used in
analyzing the problem
Satisfactorily described
the analytic concepts

12. and theories used in
analyzing the problem
Partially described the
analytic concepts and
theories used in
analyzing the problem
Did not submit or did
not provide a summary
of the problem
descriptions and
problem introduction
Category Above Standard Meets Standards Approaching
Standards Below Standards Not Evident
Word/Report:
Description of
Conclusions
ALY6010_CO5

13. Thoroughly described
the conclusions and
results obtained in the
project using a high level
of critical thinking and
reasoning
Thoroughly described
the conclusions and
results obtained in the
project
Satisfactorily described
the conclusions and
results obtained in the
project
Partially described the
conclusions and results
obtained in the project
Did not submit or did
not describe the
conclusions and results
obtained in the project

14. Word/Report:
Writing
Mechanics,
Title Page, &
References
Completely free of
errors in grammar,
spelling, and
punctuation; and
completely correct usage
of title page, citations,
and references. The
report contains a
minimum of 1000 words
There are no noticeable
errors in grammar,
spelling, and
punctuation; and
completely correct usage
of title page, citations,
and references. The
report contains a

15. minimum of 1000 words
There are very few
errors in grammar,
spelling, and
punctuation; and
completely correct usage
of title page, citations,
and references. The
report contains a
minimum of 1000 words
There are more than five
errors in grammar,
spelling, and
punctuation; or the
usage of title page,
citations, and references
are incomplete; or the
report contains less than
1000 words
Did not submit; or there
are many errors in
grammar, spelling, and

16. punctuation; or the
usage of title page,
citations, and references
are totally incomplete;
or the report contains
very few words
Running head: NAB 1
NAB 2
NAB
Name
Institutional Affiliation

17. NAB
Company Name
My company will be called Fizzy Bottles. It will be involved in
the manufacturing, sale, and distribution of non-alcoholic
beverages. The organization deals with a wide range of non-
alcoholic beverage products, such as juices, soft drinks, ready
to drinks, carbonated drinks, energy drinks, as well as bottled
waters. Headquartered in New York, New York, United States,
Fizzy Bottles plans to establish a high international presence in
the next two years. For instance, the organization will develop a
high presence in Asia-Pacific, Europe, Middle East, Africa,
Latin America, as well as North America. By using this name,
the organization plans to improve its level of brand identity,
brand image, and brand awareness. The name "Fizzy" serves as
both physical and functioning elements of the company as a
trademark for product designation. In so doing, the title sets the
organization apart by uniquely identifying it with non-alcoholic
beverages. Besides, the company's name provides the behavioral
way in which the main objectives of interest are symbolical,
intangible elements of the brand within the context of
perceiving consumers' experiences. These approaches justify the
need to differentiate a narrow and broad meaning of the brand
(Switala et al. 2018). The company's name is also important
from the consumer's point of view since it emphasizes the

18. categories of value that customers desire and expect from a
specific brand. This phenomenon can communicate and
influence emotions leading to particular needs and purchasing
experiences. "Fizzy Bottles" is a name that expresses customers'
desire for soft drinks that quenches their thirsts in pleasant
ways. Also, the organization uses its name to assure customers
that it has useful compounds with antioxidant properties.
Products
Fizzy Bottles produce and sell different types of non-alcoholic
beverages. These products include non-alcoholic beverage
products, such as juices, soft drinks, ready to drinks, carbonated
drinks, energy drinks, as well as bottled waters. Other types of
non-alcoholic beverages include enhanced waters, teas, coffees,
and sports drinks. The formulation of Fizzy is a combination of
Creatine, carbonated water, some Amino Acids (BCAAs)-
branched-chain amino acids, Turmeric, Electrolytes, and B
Vitamins but no caffeine. With no caffeine added, I can have a
young and youthful target market as well. My drink promotes
heart health and youthful exuberance. I am also considering a
Caribbean flavor maybe Guava Pear, starfruit, or sugar-apple
which I have not seen in the US Market. The main ingredient of
soft drinks that the company will utilize is carbonated water.
Carbonated waters are solutions of carbon dioxide in water
(Kregiel, 2015). The carbon dioxide bubbles provide soft drinks
with their characteristic fizzy mouthfeel. Also, this chemical

19. content plays a critical role in keeping containers pressurized.
Apart from carbonated water, non-alcoholic beverages will also
contain sweeteners. The soft drinks will undergo sweetening in
varying ways.
Furthermore, diet Fizzy drinks will utilize low-calorie
sweeteners, such as aspartame, sucralose, and saccharine. Apart
from sweeteners, the organization will use flavorings, which are
comprised of additional ingredients that will be incorporated
into the drinks to provide them their distinctive tastes. My two
flavors will be Berry Berry Blast and Sparkling Watermelon.My
focus will be on carbonated water or sparkling flavored water.
Mission
"Fizzy Bottles' mission is to optimize customers' entertainment,
refreshment, and experiences through non-alcoholic beverages.
Promote customers' satisfaction and gratification of our brand.
Develop a comprehensive continuum understanding of consumer
wants and needs to develop innovative products and designs to
meet customer satisfaction. Attract and retain customer groups,
boosting brand loyalty. "
References
Kregiel, D. (2015). Health safety of soft drinks: contents,
containers, and Micro-organisms. BioMed research
international, 2015.
Świtała, M., Gamrot, W., Reformat, B., & Bilińska-Reformat,
K. (2018). The influence of brand awareness and brand image

20. on brand equity–an empirical study of logistics service
providers. Journal of Economics & Management, 33, 96-119.
Part 1Hypergeometric Probability Distributionx- Number of
MatchesP(X = x)P(X ≤ x)TheoreticalExperimental
(Simulated)R- Standard UniformSimulated xn - Number of
SimulationsThe Experimental Mean of XThe Theoretical Mean
of X0Expected Value of X201Variance of X402SD of
X603804100520063007400850096001070011800129001310001
4151617181920
Part 2Random Sampling from a Normal PopulationR- Standard
UniformR- Frozen and SortedX - A Normal
PopulationPopulationSamplesSample 1Sample 2Sample
3Sample 4Sample 5Sample 6Sample 7Sample 8Sample 9Sample
10Sample 11Sample 12Sample 13Sample 14Sample 15Sample
16Sample 17Sample 18Sample 19Sample 20Sample 21Sample
22Sample 23Sample 24Sample 25Sample 26Sample 27Sample
28Sample 29Sample 3092Mean of XAverage of 30 Sample
means97Variance of XAverage of 30 Sample variances98SD of
XAverage of 30 Sample SDs11109510Relative Frequency
Distribution of the Population:
918371101112728781921173108610118310106891909087Samp
le Mean: 12Sample Variance10Sample
SD:8196899412939910118411107697861076109110869192951
01010109593111284821190861199749710109210981095808787

21. 94731099901183131095919596129575111093869311941010109
79486871011101087991310961010121169111010969794861091
90109293101011891011111074891010861010851010939793909
51195889912891196121010997611901094108610111011961096
95969586111297931111109210117510791088119799971010109
69173868210121092898111111098971110101072101096919911
10969310931087111086948096108785111080827711799584111
19810849810981084101010988896869982109091941087951011
10101012129711119693919511109110881010101110989489119
91212939910109791961091118910101010971011107910961010
88881010739570991010888510111090979510101110131010101
01110121195109810949595931090939311941097101079891011
10947492989610109894109911108310101011978911119911107
89397109592899484111084891096111011118510999593949710
12971192101177911210111010941184111292961182111097119
91110991011881010849797901093951187101010919589119810
12979685888310109687899593101093101085101190109588109
41011101093831099869610101269959810109499111196949510
10831082119591131111879085931196951111101090898393837
49711109010101010861011989710101010109081118283101082
11969891991110101310109910761197938674869912978197858
61112119910109810888398889011101288107710988889116787
94101110119010119075108712899388118597111111971292971
11110139584941183919010989088988410749783101195108811
10981085869910791090111010109589841094928811101070841

22. 18610841091101010119498101110801186881184109580901210
10101110951210101010901097799410101090119699101094101
11211951195967610961210991189101110959791971096109010
11107888979499111081129610101010109711761010118590107
91010837789101093961174101112971110101010109710921085
74941111101010101011101010901010101011109510109893911
09688108393969310121010951083121011101112931091109310
95101010969994811111889110101110921110111110931210981
01099121088101010881212101010111191921078769281101010
101286701010809910101010111010
Sheet 3