Question 1 (25 points)Question 1 optionsEnter the answer to.docx

Question 1 (25 points)
Question 1 options:
Enter the answer to each of the of the questions with:
T for True
F for False
a. If the variance from a data set is zero, then all the
observations in this data set must be identical.
b. P(A and Ac) = 1 where Ac is the compliment of A.
c. The mean is always equal to the median for a normal
distribution.
d. A 99% confidence interval is wider than a 95% confidence
interval of the same parameter.
e. It is easier to reject the null hypothesis if we use a smaller
significance level (alpha).
A random sample of 25 customers was chosen in UMUC
MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The

frequency distribution below shows the distribution for
checkout time (in minutes).
Checkout Time (in minutes)
Frequency
Relative Frequency
1.0 - 1.9
4
A
2.0 - 2.9
B
.4
3.0 - 3.9
C
D
4.0 - 5.9
5
E
Total
25
F
Complete the Frequency Table with the missing frequency and
relative frequency numbers.
Enter answer for "A" with 2 decimal place acueacy.
Enter answer for "B" as an integer.
Enter answer for "C" as an integer.
Enter answer for "D" as an integer.
Enter answer for "E" with 2 decimal place acueacy.
Enter answer for "F" as an integer.

Question 3 options:
This is the same table from the previous question.
Frequency
Relative Frequency
1.0 - 1.9
4
2.0 - 2.9
0.4
3.0 - 3.9
4.0 - 5.9
5
Total
25
What percentage of the checkout times was at least 3 minutes?
Enter answer as a percent without the percent sign to 0 decimal
places.
Question 4 options:

This is the same table from the previous question with the
Interval column added.
Interval
Frequency
Relative Frequency
1
1.0 - 1.9
4
2
2.0 - 2.9
0.4
3
3.0 - 3.9
4
4.0 - 5.9
5
5
Total
25
In what class interval must the median lie?
Enter answer with the appropriate Interval number.

Question 5 options:
This is the same table from the previous question.
Frequency
Relative Frequency
1.0 - 1.9
4
2.0 - 2.9
0.4
3.0 - 3.9
4.0 - 5.9
5
Total
25
Assume that the largest observation in this dataset is 4.8.
Suppose this observation were incorrectly recorded as 8.4
instead of 4.8.
Will the mean increase, decrease or remain the same?
Enter
1 for Increase
2 for Decrease
3 for Remains the same
Will the median increase, decrease or remain the same?
Enter

1 for Increase
2 for Decrease
3 for Remains the
same
Question 6 options:
A 6-faced die is rolled two times. Let A be the event that the
outcome of the first roll is an even number, and B be the event
that the outcome of the second roll is greater than 4.
How many outcomes are there in the sample space?
Enter answer as an Integer.
Question 7 options:
What is the probability that the outcome of the second roll is
greater than 4, given that the first roll is an even number?
Enter answer as a reduced fraction or a decimal rounded to 2
decimal
places.
Question 8 options:
Are A and B independent?
Enter

Y for Yes
N for No
Question 9 options:
The 5 number summary below shows the grade distribution of
two Stat 200 quizzes.
Minimum
Q1
Median
Q3
Maximum
Quiz 1
12
40
60
95
100
Quiz 2
20
35
50
90
100
Which quiz has less interquartile range in grade distribution?
a Quiz 1
b Quiz 2
c Both quizzes have the same value requested.
d It is impossible to tell using only the given information.
Answer the question by keying in the appropriate
letter.

Question 10 options:
Minimum
Q1
Median
Q3
Maximum
Quiz 1
12
40
60
95
100
Quiz 2
20
35
50
90
100
Which quiz has the greater percentage of students with grades
of 90 or over?
a Quiz 1
b Quiz 2
letter.

Minimum
Q1
Median
Q3
Maximum
Quiz 1
12
40
60
95
100
Quiz 2
20
35
50
90
100
Which quiz has lthe greatest number of students with grades
less than 60?
a Quiz 1
b Quiz 2
letter.
There are 1000 juniors in a college.
Among the 1000 juniors
200 students are taking STAT200
100 students are taking PSYC300
There are 80 students taking both courses.
What is the probability that a randomly selected junior is taking

at least one of these two courses?
Enter answer as a 2 place decimal or a reduced fraction.
There are 1000 juniors in a college.
Among the 1000 juniors
200 students are taking STAT200
100 students are taking PSYC300
There are 80 students taking both courses.
What is the probability that a randomly selected junior is
taking PSYC300, given thathe/she is takingSTAT200?
Enter answer as a 1 place decimal or a reduced fraction.
The UMUC Stat Club is selecting three offices for the new year
- a president, a vice president and a treasuer.
There are 10 qualified candidates.
How many different ways can the officers be selected?.
Imagine you are in a game show. There are 6 prizes hidden on a
game board with 10 spaces.
One prize is worth $100, another is worth $20, and four are
worth $5.
You have to pay $20 to the host if your choice is not correct.
Let the random variable x be the winning.
What is your expected winning in this game?

Enter answer to 2 decimal places.
Determine the standard deviation of x.
Round answer to 2 decimal places.
Mimi just started her tennis class three weeks ago.
On average, she is able to return 30% of her opponent’s serves.
Assume her opponent serves 10 times.
Let X be the number of returns that Mimi gets.
As we know, the distribution of X is a binomial probability
distribution.
Whatis the number of trials (n)?
Enter answer as an Integer.
What is the probability of success (p)?
Enter answer as a decimal to 2 place precision.
What is the probability of failure (q)?
Enter answer as a decimal to 2 place precision.
Answer the three questions from left to right.
Find the probability that that she returns at least 1 of the 10
serves from her opponent.
Enter answer to 3 decimal places

Do not enter answer as a percent.
How many serves can she expect to return?
Enter answer with 0 decimal paces. (integer)
The heights of pecan trees are normaily distributed with a mean
of 10 feet and a standard deviation of 2 feet.
What is the probability that a randomly selected pecan tree is
between 10 and 12 feet tall.
Enter answer as a decimal rounded to 4 decimal places.
Find the 3rd quartile of the pecan tree height distribution.
Enter answer as a decimal rounded to 2 decimal places.

If a random sample of of 100 pecan trees is selected, what is the
standard deviation of the sample mean,
Enter answer as a 1 place decimal.
Arandom sample of 225 statistic scores has a sample mean of
1500 hours.
Assume that the statistic scores have a population standard
deviation of 300 hours.
Construct a 95% confidence interval estimate of the
mean statistic scores.
Enter the lower and upper confidence limit numbers rounded to
0 decimal places.
Enter the lower confidence interval number first.
Consider the hypothesis test given by
Ho: p = 0.5
H1: p < 0.5
In a random sample of 225 subjects, the sample proportion is
found to be phat = 0.53
Determine the numerical value of the test statistic. (z)

Enter answer rounded to 3 decimal place.
Determine the p-value for this test.
Enter answer as a decimal rounded to 2 decimal points
Is there sufficient evidence to justify the rejection of Ho at an α
= .01 level?
Enter Y for Yes
Enter N for No
Consumptions of a large amount of alcohol is known to increase
reaction time.
To investigate the effects of small amounts of alcohol, reaction
time was recoded for five individuals before and after 2 ounces
of alcohol was consumed by each.
Does the data below suggest that the consumption of 2 ounces
alcohol increase mean reaction time?
.
Reaction Time (seconds)
Subject
Before the class
After the class
1
6
7
2
8

8
3
4
6
4
7
10
5
9
10
Assume we want to use a 0.10 significance level to test the
claim.
Identify the null hypothesis and the alternative hypothesis.
Enter the appropriate letter for the correct answer.
a Ho: There is no difference between reaction times before
and after the alcohol consumption.
H1: There is a difference between reaction times before
b Ho: There is a difference between reaction times before
H1: There is no difference between reaction times before and
after the alcohol consumption.
c Ho: There is no difference between the test scores before
H1: The test scores after alcohol consumption are greater than
the test scores before the alcohol consumption.
d Ho: There is no difference between the test scores before
H1: The test scores after alcohol consumption are less than
the test scores before the alcohol consumption.

Determine the numerical value of the test statistic.
Round answer to 2 decimal places.)
Determine the p-value.
Is there sufficient evidence to support the alternate hypothesis?
Enter
Y for Yes
N for No
A Stat 200 instructor is interested in whether there is any
variation in the final grades between her two classes.
Data collected from the two classes are as follows:
Section 1 n1 = 31 x1 = 75 s1 = 12
Section 2 n1 = 30 x1 = 72 s1 = 14
Her null hypothesis and alternative hypothesis are:
H0: σ1 = σ2 and Ha: σ1 < σ2
Determine the test statistic.
Determine the p-value for this test.
Enter P value rounded to 3 decimal places

Is there sufficient evidence to justify the rejection of the H0 at
the α = .01 level.
Enter Y for yes.
Enter N for no.
A random sample of 4 professional athletes produced the
following data where x is the number of endorsements the
player
has and y is the amount of money made (in millions of dollars).
x
0
1
3
5
y
1
2
3
8
Find an equation of the least squares regression line.
Round each answer to 2 decimal place with the "constant"
followed by the "slope".
Based on the above equation, what is the predicted value
of y if x = 4?
Round answer to 1 decimal place.

The UMUC Daily News reported that the color distribution for
plain M&M's was:
40% brown
20% yellow
20% orange
10% green
10% tan
Each piece of candy in a random sample of 100 plain M&m's
was clasified according to color, and the results are listed
below:
Use a 0.05 significance level to test the claim that the published
color distribution is correct.
Color
Brown
Yellow
Orange
Green
tan
Number
42
21
12
7
18

Identify the null hypothesis by selecting the appropriate letter a
or b.
a The color distribution for plain M&M 's is not in agreement
with what was reported the UMUC Daily News.
b The color distribution for plain M&M 's is in agreement
with what was reported in the UMUC Daily News.
Identify the alternative hypothesis by selecting the appropriate
letter c or d.
c The color distribution for plain M&M 's is not in agreement
with what was reported the UMUC Daily News.
d The color distribution for plain M&M 's is in agreement
with what was reported in the UMUC Daily News.
Determine the test statistic. (What is the Chi Square value
calculated from the data in the table)
Round answer to 1 decimal place.
Determine the Pvalue for this hypothesis test
Is there sufficient evidence to support the claim that the
published color distribution is correct??
Enter the appropriate letter for the correct answer.
a The Ho hypothesis is rejected. The Pvalue is less than the
significance level,

b The Ho hypothesis is not rejected. The Pvalue is greater
than than the significance level.
Running Head: BUSINESS MANAGEMENT.
1
Organizational Leadership
1
Joseph Dunn created Dunn’s Ski Emporium. In business for
twenty-five years, Dunn’s Ski Emporium is known for its state
of the art ski equipment and repairs. It offers moderate prices to
skiers in the bustling town of Vail, Colorado. The sports store
has a cozy ambiance, with a Western décor and a two story
fireplace with large windows that overlook the Rocky
Mountains. Catering to skiers, the sporting goods store helps
many skiers with their broken or challenged ski equipment.
They specialize in hourly turnaround times on repairs and one
day pick up adjustments on new equipment. This fast service
has set Dunn’s sporting goods store way above their competitors
in the area for return business both from locals and visitors.
Skiers can ski right to their door and leave from their back door
to get back on the slopes. The staff is friendly, knowledgeable,
and local. Most of them work year round.
Dunn has decided to expand his business. For some time, Dunn
noticed that the Deli next door picks up a lot of his business
from the waiting repair customers and he has seen the Deli
customers step in to purchase gloves, goggles, and other

merchandise after eating at the deli. The Deli would make an
interesting addition to his future business plans. The Deli, like
Dunn, has always done a brisk business especially in season.
Designed in a similar western motif Dunn thought he would be
able to expand easily to include the Deli into his Emporium.
The cross traffic might even increase business. However, Dunn
knows nothing about the Deli business. The deli’s owner,
George Atkins, knows and loves his business a great deal.
Dunn has known George for years and he is aware that he is
thinking of retiring in the next few years. If he buys the Deli
now and can get George to stay on at the Deli, George could
train and mentor a new managerial staff comprised of some of
his local staff and return employees who work the seasonal
rush. The trick to the mergers success would be to get everyone
on board including George. Dunn wondered how he could
ensure George’s best efforts to make the transition stable while
Dunn’s Ski Emporium grows. He cannot help but wonder how
he would feel if he were no longer in charge of his own
company. The future is bright for both businesses and Dunn
wants to keep it that way.
Dunn has decided that his best-selling point to George is to
design an organizational structure based on George’s vision and
mission. The design will have to feature and utilize George and
his employees to the best of the company’s advantage while
empowering and allowing the staff at the Deli and Dunn’s to
grow the business.
Dunn’s vision for the organization
Mr. Joseph Dunn has been in the ski business for twenty five
years. His business offers ski equipment as well as repairs.
Furthermore, the business hourly turnaround on repairs has
allow Mr. Dunn’s business to be a recognized name in the
industry and has built a clientele of loyal customers.
Nonetheless, Mr. Dunn wishes to expand his business and
purchase a nearby dely. However, Mr. Dunn has no experience
in that area, but knows that acquiring the deli would help him
achieve a greater market share. Thus, Mr. Dunn now faces the

dilemma of how to proceed on with his new endeavor. The
following analysis will employ the leadership techniques to
propose possible solutions to Mr. Dunn’s new business
endeavor.
For the organization, the vision is to increase satisfaction of
customers. By offering products with better quality, providing
quick services, providing a wider variety of products in the
product portfolio along with being hospitable and friendly to
customers, satisfaction of customers will be increased.
Furthermore, the objective of the company comprises the
expansion of its market share across the dissimilar states. This
organization, hence, is a for-profit organization. A for-profit
organization is a business with key goal of generating revenues,
as against a non-profit organization which emphasizes a goal for
example assisting the community. Being a for-profit company,
increasing the profits and sales of the company is also included
in the objective of the organization. By providing satisfaction to
customers, offering multiple services and products, selling
affordable products while keeping low costs, profits and sales
will be increased. Also, the business will make plans for
competing better, which can be attained by selling reasonable
products, promotion accompanied by providing higher quality
services and products. Furthermore, by purchasing Deli, the
company is looking for expanding into the food business. Under
the brand of Dunn’s Ski Emporium, customers will be offered
with drinks and foods after purchasing Deli. This will in turn
increase the profits and sales.
Enhancing the role as a Leader
Good leaders are supposed to ensure that they use the stipulated
values to come up with good plans that will help in achieving
organizations’ goals and objectives (Vineet Nayar, 2013). Apart
from taking total responsibility over process issues, Dunn is
also supposed to offer genuine care to his team members, teach
them and train them in matters they see important. According to
Kanaga & Kossler (2011), placing love, empowerment and
service at the heart of leadership ensures high performance in

organizations. By dedicating themselves to the welfare of their
employees, Dunn will not only be strengthening leader-
employee relationship but will also open the doors to high
performance in the organizations. Dunn can also earn his team
members’ trust, by making them feel valuable and then
assigning them meaningful challenges that tally with the
organizations’ strategic plans. This will help the team produce
extraordinary results. Alongside valuing and caring for their
team members, Dunn can always restrain from intimidating
them. According to Winter (2003), showing authentic interest in
the members’ progress outranks payment incentives as the best
technique to motivate them. Leaders are also supposed to act in
an ethical and fair way in guiding their teams. A high-
performance environment is only created when the leader is
impartial, promotes cultural diversity within the workplace and
ensuring that the team members have the spotlight most of the
time. According to Hawkins (2011), leaders are supposed to
make decisions based on the competitiveness of their employees
and not cultural differences. Dunn can also promote openness
and collaboration among the team members. Dunn can be also
tasked with setting up a mutual support culture whereby
decisions are made effectively and conflicts are resolved
amicably.
Dunn as a Change Agent
According to Sullivan (2012), some leaders always find it hard
to cope with the new environment or even come up with crucial
changes in their initial plans. This means the leader can no
longer stick to the initial plan but instead, should develop a new
strategy that will work with the new environment. Furthermore,
high performance in any team does not just come easily.
According to Kanaga et al (2011), high performance team leader
should be able to display to the team members that he or she is
not their superior but just one of them in accomplishing the
group tasks. Dunn can bring candor, vision, ability to listen and
vision. Once the team members realize that Dunn is relying on
them for high-end results, they will be able to perform highly.

Dunn can define the vision and communicate it to his group.
According to Hawkins (2011), many organizations have visions
and missions just for formality but do not really stick to them.
Dunn can ensure that once employees enter an organization,
they should be able to understand the vision well. The
organization’s vision should always be a top as the main
motivating factor to make team members stick to it. Dunn can
always communicate the vision to the team members, tackle
hurdles against goals, reinforce progress and equip them with
the necessary tools and techniques to achieve the high end
goals.
Steps for changes for the short term
First step for change in short term is to classify the benefits and
costs of acquiring Deli. Operation costs, costs of purchase, and
cost of remunerating workers will be included in the costs.
While, satisfied customers, profits as well as increased sales
will be include in benefits. After acquiring Deli, deciding
whether altering the shop’s Brand name to Dunn’s Ski
Emporium is the second change. Within Delis’ workforce,
policies in addition to the Dunn’s Ski Emporium’s culture will
be incorporated.
Steps for changes for the long term
In the long term, steps for change include the expansion of both
Dunn’s Ski Emporium and Deli into other ski resort areas, along
with the development of employee career plan that will get
capable workers both in Dunn’s Ski Emporium and Deli
diversifying and promoted into other businesses for example
hotel for tourist or sportswear.
Vision and Mission Statement
In terms of the POLC framework the mission and vision
statements are developed during the planning phase and its
purpose is to inform stakeholders, investors, as well as the
public the business’s reason for being and its long term goal.
Since the mission states the business’s reason for being and how
it intends to serve customers and employees; it should be
communicated in the form of a written statement. Thus,

everybody that is involved with the business would know what
its purpose is. Moreover, without a vision statement in place the
business’s strategy is ineffective, because the strategy derives
from both the mission and the vision statement and its intend is
to accomplish the business’s vision (Principles of Management
1.1, 2014). Thus, the following are examples of Mr. Dunn’s
mission and vision statements for his business:
Vision Statement
“To be the leading food and ski business in the state of
Colorado”
Mission Statement
“We strive to become the largest food and ski business across
the nation; using the creativity and innovation of our
employees. With the firm belief in business ethics, we have
developed and incorporated transparent practices and policies in
our organization.”
Organizational Structure
“An organizational structure indicates the method that an
organization employs to delineate lines of communication,
policies, authority and responsibilities. It determines the extent
and nature of how leadership is disseminated throughout the
organization as well as the method by which information
flows.” (Colette L. Meehan, 2015). The organizational
structure would be as follow:
The democratic organizational structure would better serve Mr.
Dunn’s new business. This is because such structure would not
only allow but encourage the employees’ participation. Mr.
Dunn’s new business success will be dependent upon its
employees’ knowledge, customer service, and sense of urgency
to comply with the assigned work. Thus, by employing this
structure the employees will feel valuable and willing to
collaborate to fulfill the business’s mission.
The Organizational Culture That Supports Dunn’s Vision

Being the leading ski and food business in the Colorado state is
the vision of the company, which can be attained by providing
the appropriate business culture to workers. Culture styles, for
example, clan style and laissez-faire promote contribution
among employees and corporation. Thus, the clan culture in Mr.
Dunn’s new business would complement its democratic
structure. Such culture would encourage the employees to arise
with new ideas that are valuable for the business both in the
long and the short term. Such ideas comprise, introduction of a
newer product or service, ways for lowering the costs of the
company, and ways for attracting new customers. The clan
culture would empower employees by allowing them to be
participative with valuable ideas (Ari Weinzweig, 2015).
Thus the clan culture would help to achieve the business’s
mission. By empowering the employees, they will feel a sense
of belonging that would help to provide and offer a convenient
services and products of affordable and high quality, along with
offering the services in an appropriate way. Furthermore, such
culture would encourage the employees to make sure that the
clients are quickly serviced, whether it is solving a complaint or
selling a product.
Strengthening the Vision
For attaining the vision, Dunn needs to
· Act in a moral way.
· Concentrate on workers, the services and products, and finally
the customers.
· Use the 4 Ps’ (product, price, place and promotion).
· Classify and exploit opportunities in the marketplace.
· Involve workers in making of decisions.
The Critical Elements
The following critical elements must be kept in mind in
order to have a successful venture:
The first critical element is to offering the services and products
that must be cheaper as compare to those that are accessible in

the marketplace already. This will assist in attracting the new
customers along with retaining the old customers. Also, it will
allow the business for competing better in the marketplace as
compare to its rivals. Secondly, with the intention of remaining
profitable, there is a need of selling services and products above
their costs of production. Finally, there is a need of providing
good salary to workers with the intention of retaining them, and
also there is a need of providing training to employees that can
impact their abilities positively. Through the proper
implementation of the mission and vision statement as well as
the proper development of a democratic organizational structure
and a clan organizational culture which would encourage and
reward employees’ participation, Mr. Dunn can rest assure that
the critical elements would not only be met, but the company’s
vision will be achieved.
References
Hawkins, P. (2011). Leadership team coaching: Developing
collective transformational leadership. NY: Kogan Page
Publishers.
Kanaga, K. & Kossler, M. (2011). How to form a team: 5 keys
to high performance. LA: Centre for Creative Leadership.
Sullivan, J. (2012). Multiunit leadership: The 7 stages of
building a high-performing partnerships and teams. Washington
D.C: Business & Economics.
Winter, G. (2003). High performance leadership: Creating,
leading and living in high performance world. NY: John Wiley
& Sons.Ari Weinzweig, 2015. Five Steps to Building an
Organizational Culture. Retrieved from
http://www.zingtrain.com/org-culture-steps
Colette L. Meehan, 2015. Flat vs. Hierarchical Organization
Structure, Retrieved from http://smallbusiness.chron.com/flat-
vs-hierarchical-organizational-structure-724.html
Unknown (2014). Principles of Management 1.1. Washington,
D.C.: The Saylor Foundation.
Vineet Nayar, 2013. Three Differences Between Managers and

Leaders. Retrieved from
https://hbr.org/2013/08/tests-of-a-leadership-transiti

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