Statistics- Given that Z is a standard normal random variable

by | Aug 20, 2025 | Business

Question
1(2 points)

Question 1 unsaved


Given that Z is a standard normal random variable, P(-1.0equationZequation1.5) is

Question 1 options:

0.8413

0.0919

0.9332

0.7745

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Question 2(2 points)

Question 2 unsaved

There are two types of random variables, they are

Question 2 options:

real
and unreal

exhaustive
and mutually exclusive

complementary
and cumulative

discrete
and continuous

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Question 3(2 points)

Question 3 unsaved

In a normal distribution, changing the standard deviation:

Question 3 options:

makes
the curve more dense

splits
the distribution to two curves

shifts
the curve left or right

makes
the curve more or less spread out

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Question 4(2 points)

Question 4 unsaved

If Z is a standard normal random variable, the
area between z = 0.0 and z =1.30 is 0.4032,
while the area between z = 0.0 and z = 1.50
is 0.4332. What is the area between z = -1.30 and z =
1.50?

Question 4 options:

0.8364

0.0968

0.0300

0.0668

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Question 5(2 points)

Question 5 unsaved

Given that the random variable X is normally
distributed with a mean of 80 and a standard deviation of 10, P(85equationXequation90) is

Question 5 options:

0.3413

0.1915

0.1498

0.5328

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Question 6(2 points)

Question 6 unsaved

Which of the following statements are true?

Question 6 options:

Probabilities
can either be positive or negative.

Probabilities
must be nonnegative.

Probabilities
can be any positive value.

Probabilities
must be negative.

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Question 7(2 points)

Question 7 unsaved

The standard deviationequationof a probability distribution is a:

Question 7 options:

measure
of relative likelihood

measure
of variability of the distribution

measure
of central location

measure
of skewness of the distribution

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Question 8(2 points)

Question 8 unsaved

Given that Z is a standard normal variable, the
value z for which P(Zequationz) = 0.2580 is

Question 8 options:

0.242

-0.65

0.758

0.70

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Question 9(3 points)

Question 9 unsaved

Assume that a company makes wooden picture frames. Frame style 1
takes 2 hours of skilled labor and 3 linear feet of wood. If the company had 40
hours of skilled labor and 48 linear feet of wood that can be used each week,
what is the largest quantity of this item that the company will be able to
produce given these resource constraints?

Question 9 options:

19

13

16

22

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Question 10(2 points)

Question 10 unsaved

Related to sensitivity analysis in linear programming, when the
profit increases with a unit increase in a resource, this change in profit is
referred to as the:

Question 10 options:

sensitivity
price

add-in
price

additional
profit

shadow
price

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Question 11(3 points)

Question 11 unsaved

Consider the following
linear programming problem:

Minimize 5x1+ 6x2

Subject to
x1+ 2x2 > 12
3x1 + 2x2> 24
3x1 + x2> 15

x1, x2 > 0

What are the optimal
decision variables values?

Question 11 options:

(5,4)

(6,3)

(5,3)

(4,5)

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Question 12(3 points)

Question 12 unsaved

One of the things that can go wrong with a linear programming
problem is that it may not be possible to find a set of points that satisfy all
of the constraints in the problem. This type of problem is said to be:

Question 12 options:

redundant

unbounded

inconsistent

infeasible

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Question 13(3 points)

Question 13 unsaved

In using a spreadsheet to solve linear programming problems, the
changing cells represent the:

Question 13 options:

decision
variables

constraints

value
of the objective function

total
cost of the model

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Question 14(3 points)

Question 14 unsaved

When formulating an LP spreadsheet model, the changing cells
play the role of the decision variables, and the values in these cells can be
changed to optimize the objective function.

Question 14 options:

True

False

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Question 15(3 points)

Question 15 unsaved

When formulating an LP
spreadsheet model, target objective cell that contains the value of the
objective function.

Question 15 options:

True

False

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Question 16(3 points)

Question 16 unsaved

Sensitivity analysis is
to see how, or if the optimal solution to an LP problem changes as we change
one or more model inputs.

Question 16 options:

True

False

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Question 17(3 points)

Question 17 unsaved

S&V Industries manufactures book cases. Different sizes of
cases are kept in inventory. The company has 80 man-hours and 36 pounds of wood
available each day. 2 pounds of wood are used to produce case x1while
6 pounds of woods are used for case x2. Given that the optimal
solution is x1 = 6 and x2 = 3.2, how much wood
will be unused if the optimal number of bookcases are produced?

Question 17 options:

none

4.8
pounds

8
pounds

cannot
be determined with the information given.

Do
Not Know

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Question 18(3 points)

Question 18 unsaved

In a production process, the diameter measures of manufactured
o-ring gaskets are known to be normally distributed with a mean diameter of 80
mm and a standard deviation of 3 mm. Any o-ring measuring 75 mm or less in
diameter is defective and cannot be used. Using Excel, determine the percent or
proportion of defective o-rings that will be produced.

(Enter the value in either decimal or percent notation. If using decimal
notation, enter the value using 4 places to the right of the decimal. If using
percent notation, go two places to the right of the decimal. For example,
decimal notation might be 0.0768 and percent notation would be 7.68. Do not
enter words or symbols)

Question 18 options:

Spell check

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Question 19(3 points)

Question 19 unsaved

Use the data below to
determine the relationship between x and y. Choose the best description of the
relationship below.

x y9.5 370 10.0 360 10.0 400 10.0 400 10.3 420 9.1 350 8.6 310

Question 19 options:

Positive Linear

Negative Linear

No Relationship Exists

Do Not Know

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Question 20(3 points)

Question 20 unsaved

Given the following linear programming model:
minimize C = 5x1 + 4x2
subject to
6x1 + 10x2equation300
10x1+ 4x2equation200
x1, x2equation0

Using the Excel Solver tool, its solution as correctly rounded is:

Question 20 options:

x1 =
20, x2 = 0

x1 =
10.53, x2 = 23.68

x1 =
56, x2 = 0

x1 =
1, x2 = 30

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Question 21(3 points)

Question 21 unsaved

Many airline flights are late for arrival. The histogram below
displays the number of minutes a sample of schedules flights was late. The
number above each bar is the frequency. For example, the second interval
reveals that 5 flights were at least 10 minutes late but less than 20 minutes
late.What percent of flights were at least 10 minutes late but less than 20
minutes late?(Enter your value in percent notation. For example, enter the
value 30% as either 30 or 30%. Do not enter words, spaces, decimal point, or
other marks or symbols)
https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-Exam%20S09/histo1.jpg?_&d2lSessionVal=ItVcFJZYRZ3mk8iNh9dUSdR55

Question 21 options:

Spell check

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Question 22(3 points)

Question 22 unsaved

Karim’s Oak Furniture Company manufactures oak tables and
chairs. To manufacture the chairs and tables, the wood must be cut, glued, and
finished. The labor requirements for the three steps are in the table below, as
well as the profit for each table and chair. The available time for the labor
requirements are 40 hours for cutting, 40 hours for gluing, and 40 hours for
finishing.Karim wants to determine the number of tables and chairs to
manufacture in order to maximize profit.What are the decision variables?
https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-Exam%20S09/karim_table_p_1_a.jpg?_&d2lSessionVal=ItVcFJZYRZ3mk8iNh9dUSdR55

Question 22 options:

x1 =
the number of hours to make a table,x2 = the number of hours
to make a chair

x1 =
the number of hours required to cut, x2 = the number of hours
required to glue, X3 = the number of hours required to finish

x1 =
the number of tables, x2 = the number of chairs

x1=
the profit per table, x2 = the profit per chair

Do
Not Know

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Question 23(3 points)

Question 23 unsaved

For the data set below, use Excel to determine the slope, the
rate of change of y for a one-unit change in x.
https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-Exam%20S09/regr_data_table.gif?_&d2lSessionVal=ItVcFJZYRZ3mk8iNh9dUSdR55

Question 23 options:

Spell check

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Question 24(3 points)

Question 24 unsaved

A variable is classified as ordinal if:

Question 24 options:

there
is a natural ordering of categories

there
is no natural ordering of categories

the
data arise from continuous measurements

we
track the variable through a period of time

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Question 25(3 points)

Question 25 unsaved

Gender and State are examples of which type of data?

Question 25 options:

Discrete
data

Continuous
data

Categorical
data

Ordinal
data

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Question 26(3 points)

Question 26 unsaved

The correlation coefficient is always a value between

Question 26 options:

–
1 and 0

0
and +1

0.0
and 100

-1
and +1

-1
and 100

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Question 27(3 points)

Question 27 unsaved

Which of the following are the three most common measures of central
location?

Question 27 options:

Mean,
median, and mode

Mean,
variance, and standard deviation

Mean,
median, and variance

Mean,
median, and standard deviation

First
quartile, second quartile, and third quartile

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Question 28(3 points)

Question 28 unsaved

Which of the following are considered measures of association?

Question 28 options:

Mean
and variance

Variance
and correlation

Correlation
and covariance

Covariance
and variance

First
quartile and third quartile

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Question 29(3 points)

Question 29 unsaved

The median can also be described as:

Question 29 options:

the
middle observation when the data values are arranged in ascending order

the
second quartile

the
50th percentile

All
of the above

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Question 30(2 points)

Question 30 unsaved

In regression analysis, the variables used to help explain or
predict the response variable are called the

Question 30 options:

independent
variables

dependent
variables

regression
variables

statistical
variables

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Question 31(2 points)

Question 31 unsaved

In regression analysis, if there are several explanatory
variables, it is called:

Question 31 options:

simple
regression

multiple
regression

compound
regression

composite
regression

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Question 32(2 points)

Question 32 unsaved

In regression analysis, the variable we are trying to explain or
predict is called the

Question 32 options:

independent
variable

dependent
variable

regression
variable

statistical
variable

residual
variable

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Question 33(2 points)

Question 33 unsaved

The coefficient of determination (https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-Exam%20S09/eq_821afc.gif?_&d2lSessionVal=ItVcFJZYRZ3mk8iNh9dUSdR55) ranges from

Question 33 options:

-1
to +1

-2
to +2

-1
to 0

0
to +1

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Question 34(2 points)

Question 34 unsaved

The coefficient of determination (https://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-Exam%20S09/eq_821add.gif?_&d2lSessionVal=ItVcFJZYRZ3mk8iNh9dUSdR55) can be interpreted as
the fraction (or percent) of variation of the

Question 34 options:

explanatory
variable explained by the independent variable

explanatory
variable explained by the regression line

response
variable explained by the regression line

error
explained by the regression line

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Question 35(2 points)

Question 35 unsaved

In a multiple regression analysis, there are 25 data points and
5 independent variables. If the sum of the squared differences between observed
and predicted values of y is 160, then standard error of estimate, denoted
byhttps://go.view.usg.edu/content/enforced/957070-WMBA6040-Quant-Summer2015-Wang-C56/RspQ-Exam%20S09/eq_82185e.gif?_&d2lSessionVal=ItVcFJZYRZ3mk8iNh9dUSdR55will be:

Question 35 options:

2.530

3.464

2.902

5.657

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Question 36(2 points)

Question 36 unsaved

Which of the following is not one of the
summary measures for forecast errors that is commonly used?

Question 36 options:

MAE
(mean absolute error)

MFE
(mean forecast error)

RMSE
(root mean square error)

MAPE
(mean absolute percentage error)

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Question 37(2 points)

Question 37 unsaved

Winters’ model differs from Holt’s model and simple exponential
smoothing in that it includes an index for:

Question 37 options:

cyclical
fluctuations

trend

residuals

seasonality

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Question 38(2 points)

Question 38 unsaved

The forecast error is the difference between

Question 38 options:

the
average value and the expected value of the response variable

the
actual value and the forecast

the
explanatory variable value and the response variable value

this
period’s value and the next period’s value

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Question 39(2 points)

Question 39 unsaved

Holt’s model differs from simple exponential smoothing in that
it includes a term for:

Question 39 options:

residuals

cyclical
fluctations

seasonality

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