Question 1

From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. Which of the following distributions would you use to
Determine the probability that out of the 8 new cars it just received that, when each is tested, no
More than 2 of the cars have defective radios?

Accepted Answer

A)  Hypergeometric distribution. 
B)  Poisson distribution. 
C)  Uniform distribution. 
D)  Binomial distribution.

Question 2

A wheel spinning game is played with a special wheel with 24 equal segments that determine the dollar values of a single spin. Which of the following distributions can best be used to compute
The probability of winning a specific dollar value in a single spin?

Accepted Answer

A)  Uniform distribution 
B)  Binomial distribution 
C)  Normal distribution 
D)  Exponential distribution

Question 3

SCENARIO 17-15
The tree diagram below shows the results of the classification tree model that has been constructed to
predict the probability of a cable company's customers who will switch ("Yes" or "No") into its
bundled program offering based on the price ($30, $40, $50, $60) and whether the customer spends
more than 5 hours a day watching TV ("Yes" or "No") using the data set of 100 customers collected
from a survey.  
-Referring to Scenario 17-15, the highest probability of switching is predicted to
occur among customers who watch more than 5 hours of TV a day and are offered the bundled
price of between $30 and $40.

Accepted Answer

A) True 
 B)False

Question 4

SCENARIO 17-8
The superintendent of a school district wanted to predict the percentage of students passing a sixth-
grade proficiency test. She obtained the data on percentage of students passing the proficiency test
(% Passing), daily mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state. Following is the multiple regression output with $Y = \%$ Passing as the dependent variable, $X _ { 1 } = \%$ Attendance, $X _ { 2 } =$ Salaries and $X _ { 3 } =$ Spending:

$\begin{array}{lr}
\hline{\text { Regression Statistics }} \
\hline \text { Multiple R } & 0.7930 \
\text { R Square } & 0.6288 \
\text { Adjusted R } & 0.6029 \
\text { Square } & \
\text { Standard } & 10.4570 \
\text { Error } & \
\text { Observations } & 47 \
\hline
\end{array}$

ANOVA

$\begin{array}{lrrrrrr}
\hline & \text { Coefficients } & \begin{array}{c}
\text { Standard } \
\text { Error }
\end{array} & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & -753.4225 & 101.1149 & -7.4511 & 0.0000 & -957.3401 & -549.5050 \
\text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \
\text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \
\text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \
\hline
\end{array}$
-Referring to Scenario 17-8, which of the following is the correct null hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency
Test, taking into account the effect of all the other independent variables? a) $H _ { 0 } : \beta _ { 0 } = 0$
b) $H _ { 0 } : \beta _ { 1 } = 0$
c) $H _ { 0 } : \beta _ { 2 } = 0$
d) $H _ { 0 } : \beta _ { 3 } = 0$

Accepted Answer

The answer of SCENARIO 17-8
The superintendent of a school district...

Question 5

Suppose the probability of finding a defective spot in an area on a piece of glass is the ratio of that area to the total area of the glass and the probability is the same across the whole glass.
Which of the following distributions would you use to determine the probability of finding a
Defective spot in a randomly selected one square inch area on a piece of 10 feet by 10 feet glass?

Accepted Answer

A)  Normal distribution. 
B)  Poisson distribution. 
C)  Uniform distribution. 
D)  Exponential distribution.

Question 6

SCENARIO 17-8
The superintendent of a school district wanted to predict the percentage of students passing a sixth-
grade proficiency test. She obtained the data on percentage of students passing the proficiency test
(% Passing), daily mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state. Following is the multiple regression output with $Y = \%$ Passing as the dependent variable, $X _ { 1 } = \%$ Attendance, $X _ { 2 } =$ Salaries and $X _ { 3 } =$ Spending:

$\begin{array}{lr}
\hline{\text { Regression Statistics }} \
\hline \text { Multiple R } & 0.7930 \
\text { R Square } & 0.6288 \
\text { Adjusted R } & 0.6029 \
\text { Square } & \
\text { Standard } & 10.4570 \
\text { Error } & \
\text { Observations } & 47 \
\hline
\end{array}$

ANOVA

$\begin{array}{lrrrrrr}
\hline & \text { Coefficients } & \begin{array}{c}
\text { Standard } \
\text { Error }
\end{array} & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & -753.4225 & 101.1149 & -7.4511 & 0.0000 & -957.3401 & -549.5050 \
\text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \
\text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \
\text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \
\hline
\end{array}$
-Referring to Scenario 17-8, which of the following is the correct alternative hypothesis to test whether daily mean of the percentage of students attending class has any effect on percentage of
Students passing the proficiency test, taking into account the effect of all the other independent
Variables? a) $H _ { 1 } : \beta _ { 0 } \neq 0$
b) $H _ { 1 } : \beta _ { 1 } \neq 0$
c) $H _ { 1 } : \beta _ { 2 } \neq 0$
d) $H _ { 1 } : \beta _ { 3 } \neq 0$

Accepted Answer

The answer of SCENARIO 17-8
The superintendent of a school district...

Question 7

A contractor wants to forecast the number of contracts in future quarters, using quarterly data on number of contracts over the last 10 years. Which of the following would be the most
Appropriate analysis to perform?

Accepted Answer

A)  Autoregressive modeling. 
B)  One-way ANOVA. 
C)  Least-squares forecasting with monthly or quarterly data. 
D)  Two-way ANOVA.

Question 8

SCENARIO 17-10 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: $1 =$ married, $0 =$ otherwise), a dummy variable for head of household (Head: $1 =$ yes, $0 =$ no) and a dummy variable for management position (Manager: $1 =$ yes, $0 =$ no). We shall call this Model 1. The coefficient of partial determination ( $R _ { \mathrm { y } } ^ { 2 }$ (All raiables excopt $j$ ) ) of each of the 6 predictors are, respectively, $0.2807$, $0.0386,0.0317,0.0141,0.0958$, and $0.1201$.

$\begin{array}{lr}
\hline{\text { Regression Statistics }} \
\hline \text { Multiple R } & 0.7035 \
\text { R Square } & 0.4949 \
\text { Adjusted R } & 0.4030 \
\text { Square } & \
\text { Standard } & 18.4861 \
\text { Error } & \
\text { Observations } & 40 \
\hline
\end{array}$
 $\text { ANOVA }$

$$\begin{array}{l}
\begin{array} { l r r r r r r } 
\hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \
\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \
\text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \
\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \
\text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \
\text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \
\text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \
\hline
\end{array}
\end{array}$$
-Referring to Scenario 17-10 Model 1, which of the following is a correct statement?

Accepted Answer

A)  49.49% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker, the number of years of education
Received, the number of years at the previous job, marital status, whether the worker is
The head of household and whether the worker is a manager. 
B)  49.49% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker, the number of years of education
Received, the number of years at the previous job, marital status, whether the worker is
The head of household and whether the worker is a manager after adjusting for the
Number of predictors and sample size. 
C)  49.49% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker, the number of years of education
Received, the number of years at the previous job, marital status, whether the worker is
The head of household and whether the worker is a manager after adjusting for the level of
Significance 
D)  49.49% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker, the number of years of education
Received, the number of years at the previous job, marital status, whether the worker is
The head of household and whether the worker is a manager holding constant the effect of
All the independent variables.

Question 9

Some business analytics involve starting with many variables, followed by filtering
the data by exploring specific combinations of categorical values or numerical range. In Excel, this
approach is mimicked by using gauges.

Accepted Answer

A) True 
 B)False

Question 10

SCENARIO 17-9
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a
car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables
as the independent variables are presented below.  
-Referring to Scenario 17-9, which of the following assumptions is most likely violated based on the residual plot for HP?

Accepted Answer

A)  Linearity. 
B)  Normality of errors. 
C)  Independence of errors. 
D)  None.

Question 11

Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to
Compare the 4 procedures, and collects the following numbers of patients from their own records:  $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Procedure }$
$\begin{array}{l|cccc||c} 
& \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \
\hline \hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \
\text { Return } & 11 & 15 & 9 & 11 & 46 \
\hline \hline \text { Total } & 38 & 56 & 30 & 18 & 142
\end{array}$

Which of the following tests will be the most appropriate to find out which of the 4 procedures is the most effective?
a) $\chi ^ { 2 }$ test for difference in proportions.
b) $Z$ test for difference in proportions.
c) One-way ANOVA $F$ test for differences among more than two means
d) The Marascuilo procedure.

Accepted Answer

The answer of Four surgical procedures currently are used to...

Question 12

The weight of a randomly selected cookie from a production line can most likely be modeled by which of the following distributions?

Accepted Answer

A)  Uniform distribution. 
B)  Poisson distribution. 
C)  Normal distribution. 
D)  Exponential distribution.

Question 13

SCENARIO 17-12
The marketing manager for a nationally franchised lawn service company would like to study the
characteristics that differentiate home owners who do and do not have a lawn service. A random
sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have
a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available
concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn
size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Atitude 0
= unfavorable, 1 = favorable), number of teenagers in the household (Teenager), and age of the head
of the household (Age).
The Minitab output is given below: 
-Referring to Scenario 17-12, there is not enough evidence to conclude that Age
makes a significant contribution to the model in the presence of the other independent variables at
a 0.05 level of significance.

Accepted Answer

A) True 
 B)False

Question 14

SCENARIO 17-8
The superintendent of a school district wanted to predict the percentage of students passing a sixth-
grade proficiency test. She obtained the data on percentage of students passing the proficiency test
(% Passing), daily mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state. Following is the multiple regression output with $Y = \%$ Passing as the dependent variable, $X _ { 1 } = \%$ Attendance, $X _ { 2 } =$ Salaries and $X _ { 3 } =$ Spending:

$\begin{array}{lr}
\hline{\text { Regression Statistics }} \
\hline \text { Multiple R } & 0.7930 \
\text { R Square } & 0.6288 \
\text { Adjusted R } & 0.6029 \
\text { Square } & \
\text { Standard } & 10.4570 \
\text { Error } & \
\text { Observations } & 47 \
\hline
\end{array}$

ANOVA

$\begin{array}{lrrrrrr}
\hline & \text { Coefficients } & \begin{array}{c}
\text { Standard } \
\text { Error }
\end{array} & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & -753.4225 & 101.1149 & -7.4511 & 0.0000 & -957.3401 & -549.5050 \
\text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \
\text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \
\text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \
\hline
\end{array}$
-Referring to Scenario 17-8, which of the following is the correct alternative hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the
Proficiency test, taking into account the effect of all the other independent variables? a) $H _ { 1 } : \beta _ { 0 } \neq 0$
b) $H _ { 1 } : \beta _ { 1 } \neq 0$
c) $H _ { 1 } : \beta _ { 2 } \neq 0$
d) $H _ { 1 } : \beta _ { 3 } \neq 0$

Accepted Answer

The answer of SCENARIO 17-8
The superintendent of a school district...

Question 15

A professor of economics at a small Texas university wanted to determine what year in school
students were taking his tough economics course. Data were collected on the class status
("freshman", "sophomore", "junior" or "senior") of 50 students enrolled in one of his economics
course. A side-by-side bar chart can be used to present this information.

Accepted Answer

A) True 
 B)False

Question 16

SCENARIO 17-9
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a
car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables
as the independent variables are presented below.  
-Referring to Scenario 17-9, the 0 to 60 miles per hour acceleration time of a
coupe is predicted to be 0.7679 seconds higher than that of a sedan.

Accepted Answer

A) True 
 B)False

Question 17

SCENARIO 17-4
You decide to predict gasoline prices in different cities and towns in the United States for your term
project. Your dependent variable is price of gasoline per gallon and your explanatory variables are
per capita income, the number of firms that manufacture automobile parts in and around the city, the
number of new business starts in the last year, population density of the city, percentage of local taxes
on gasoline, and the number of people using public transportation. You collected data of 32 cities
and obtained a regression sum of squares SSR= 122.8821. Your computed value of standard error of
the estimate is 1.9549.
-Referring to Scenario 17-4, what is the value of the coefficient of multiple determination?

Accepted Answer

A)  0.2225 
B)  0.4576 
C)  0.5626 
D)  0.6472

Question 18

SCENARIO 17-10 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: $1 =$ married, $0 =$ otherwise), a dummy variable for head of household (Head: $1 =$ yes, $0 =$ no) and a dummy variable for management position (Manager: $1 =$ yes, $0 =$ no). We shall call this Model 1. The coefficient of partial determination ( $R _ { \mathrm { y } } ^ { 2 }$ (All raiables excopt $j$ ) ) of each of the 6 predictors are, respectively, $0.2807$, $0.0386,0.0317,0.0141,0.0958$, and $0.1201$.

$\begin{array}{lr}
\hline{\text { Regression Statistics }} \
\hline \text { Multiple R } & 0.7035 \
\text { R Square } & 0.4949 \
\text { Adjusted R } & 0.4030 \
\text { Square } & \
\text { Standard } & 18.4861 \
\text { Error } & \
\text { Observations } & 40 \
\hline
\end{array}$
 $\text { ANOVA }$

$$\begin{array}{l}
\begin{array} { l r r r r r r } 
\hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \
\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \
\text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \
\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \
\text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \
\text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \
\text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \
\hline
\end{array}
\end{array}$$
-Referring to Scenario 17-10 Model 1, what is the value of the test statistic when testing whether
age has any effect on the number of weeks a worker is unemployed due to a layoff while holding
constant the effect of all the other independent variables?

Accepted Answer

The answer of SCENARIO 17-10 Given below are results from...

Question 19

SCENARIO 17-10 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: $1 =$ married, $0 =$ otherwise), a dummy variable for head of household (Head: $1 =$ yes, $0 =$ no) and a dummy variable for management position (Manager: $1 =$ yes, $0 =$ no). We shall call this Model 1. The coefficient of partial determination ( $R _ { \mathrm { y } } ^ { 2 }$ (All raiables excopt $j$ ) ) of each of the 6 predictors are, respectively, $0.2807$, $0.0386,0.0317,0.0141,0.0958$, and $0.1201$.

$\begin{array}{lr}
\hline{\text { Regression Statistics }} \
\hline \text { Multiple R } & 0.7035 \
\text { R Square } & 0.4949 \
\text { Adjusted R } & 0.4030 \
\text { Square } & \
\text { Standard } & 18.4861 \
\text { Error } & \
\text { Observations } & 40 \
\hline
\end{array}$
 $\text { ANOVA }$

$$\begin{array}{l}
\begin{array} { l r r r r r r } 
\hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \
\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \
\text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \
\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \
\text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \
\text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \
\text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \
\hline
\end{array}
\end{array}$$
-Referring to Scenario 17-10 Model 1, what is the value of the test statistic when testing whether
being married or not makes a difference in the mean number of weeks a worker is unemployed
due to a layoff while holding constant the effect of all the other independent variables?

Accepted Answer

The answer of SCENARIO 17-10 Given below are results from...

Question 20

SCENARIO 17-1
A real estate builder wishes to determine how house size (House) is influenced by family income
(Income), family size (Size), and education of the head of household (School). House size is
measured in hundreds of square feet, income is measured in thousands of dollars, and education is in
years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel
output is provided below: SUMMARY OUTPUT
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \ \text { R Square } & 0.748 \ \text { Adjusted R Square } & 0.726 \ \text { Standard Error } & 5.195 \ \text { Observations } & 50 \end{array}$
ANOVA
$\begin{array} { l c c c c c } & d f & \text { SS } & \text { MS } & F & \text { Signif } F \ \text { Regression } & & 3605.7736 & 1201.9245 & & 0.0000 \ \text { Residual } & & 1214.2264 & 26.3962 & & \ \text { Total } & 49 & 4820.0000 & & & \end{array}$

$\begin{array} { l c l c c } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 \ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 \end{array}$
-Referring to Scenario 17-1, suppose the builder wants to test whether the coefficient on Income is significantly different from 0. What is the value of the relevant t-statistic?

Accepted Answer

A)  5.286 
B)  5.195 
C)  3.945 
D)  - 1.509

Exam 17: Getting Ready to Analyze Data

A wheel spinning game is played with a special wheel with 24 equal segments that determine the dollar values of a single spin. Which of the following distributions can best be used to compute The probability of winning a specific dollar value in a single spin?

A contractor wants to forecast the number of contracts in future quarters, using quarterly data on number of contracts over the last 10 years. Which of the following would be the most Appropriate analysis to perform?

Some business analytics involve starting with many variables, followed by filtering the data by exploring specific combinations of categorical values or numerical range. In Excel, this approach is mimicked by using gauges.

The weight of a randomly selected cookie from a production line can most likely be modeled by which of the following distributions?