Question 1

The Excel function NORM.DIST finds probabilities for the standard normal distribution.

Accepted Answer

A) True 
 B)False  False

Question 2

What are the properties of a probability mass function?

Accepted Answer

A probability mass function has the properties that (1) the probability of each outcome must be between 0 and 1 and (2) the sum of all probabilities must add to 1 ; that is,

0 \leq f\left(\mathrm{x}_{i}\right) \leq 1

, for all

i

\sum_{i} f\left(x_{i}\right)=1

$\sum_{i} f\left(x_{i}\right)=1$

Question 3

Which of the following is true about using sample data?

Accepted Answer

A) All samples have the same characteristics and hence always adequately represent the underlying population. 
B) It can limit the ability to predict uncertain events that may occur because potential values outside the range of the sample data are not included. 
C) It is better to use sample data than trying to identify the underlying probability distribution and fitting a theoretical distribution to it. 
D) Using sample data in a decision model increases the ability to predict uncertain events. 
A) All samples have the same characteristics and hence always adequately represent the underlying population. 
B) It can limit the ability to predict uncertain events that may occur because potential values outside the range of the sample data are not included. 
C) It is better to use sample data than trying to identify the underlying probability distribution and fitting a theoretical distribution to it. 
D) Using sample data in a decision model increases the ability to predict uncertain events. B

Question 4

Use the data given below to answer the following question(s).
15 students were asked to choose between the broad categories of Arts, Science, and Math as their preferred area of study.
 $\begin{array}{|c|c|c|}
\hline \text { Respondent } & \text { Gender } & \text { Preference } \
\hline 1 & \text { Female } & \text { Art.s } \
\hline 2 & \text { Male } & \text { Science } \
\hline 3 & \text { Male } & \text { Math } \
\hline 4 & \text { Female } & \text { Art.s } \
\hline 5 & \text { Female } & \text { Math } \
\hline 6 & \text { Male } & \text { Science } \
\hline 7 & \text { Male } & \text { Math } \
\hline 8 & \text { Male } & \text { Math } \
\hline 9 & \text { Female } & \text { Art.s } \
\hline 10 & \text { Male } & \text { Art.s } \
\hline 11 & \text { Male } & \text { Science } \
\hline 12 & \text { Female } & \text { Science } \
\hline 13 & \text { Female } & \text { Math } \
\hline 14 & \text { Male } & \text { Art.s } \
\hline 15 & \text { Female } & \text { Art.s }
\end{array}$
-What is the probability that a respondent prefers Science given that the respondent is female?

Accepted Answer

A) $\frac{1}{15}$ 
B) $\frac{1}{7}$ 
C) $\frac{7}{15}$ 
D) $\frac{4}{7}$ 
A) $\frac{1}{15}$ 
B) $\frac{1}{7}$ 
C) $\frac{7}{15}$ 
D) $\frac{4}{7}$

Question 5

The exponential distribution:

Accepted Answer

A) has the density function f (x)= e⁻λˣ , for x ≥ 0. 
B) models the time between randomly occurring events. 
C) has an expected value λ. 
D) is described by the familiar bell-shaped curve. 
A) has the density function f (x)= e⁻λˣ , for x ≥ 0. 
B) models the time between randomly occurring events. 
C) has an expected value λ. 
D) is described by the familiar bell-shaped curve.

Question 6

Which of the following will hold true if events X and Y are independent?

Accepted Answer

A) P(X)= P(Y)× P(X and Y) 
B) P(Y)= P(X|Y) 
C) P(X and Y)= [P(X)+ P(Y)] - P(X or Y) 
D) P(X)= P(X|Y) 
A) P(X)= P(Y)× P(X and Y) 
B) P(Y)= P(X|Y) 
C) P(X and Y)= [P(X)+ P(Y)] - P(X or Y) 
D) P(X)= P(X|Y)

Question 7

Which of the following characterizes a random variable having two possible outcomes, each with a constant probability of occurrence?

Accepted Answer

A) Beta distribution 
B) Bernoulli distribution 
C) Poisson distribution 
D) Binominal distribution 
A) Beta distribution 
B) Bernoulli distribution 
C) Poisson distribution 
D) Binominal distribution

Question 8

Which of the following is true about the classical definition of probability?

Accepted Answer

A) It is based on judgment and experience. 
B) If the process that generates the outcomes is known, probabilities can be deduced from theoretical arguments. 
C) The probability that an outcome will occur is simply the relative frequency associated with that outcome. 
D) It is based on observed data. 
A) It is based on judgment and experience. 
B) If the process that generates the outcomes is known, probabilities can be deduced from theoretical arguments. 
C) The probability that an outcome will occur is simply the relative frequency associated with that outcome. 
D) It is based on observed data.

Question 9

Which of the following is a continuous random variable?

Accepted Answer

A) the outcomes of rolling two dice 
B) the time to complete a specific task 
C) the number of new hires in a year 
D) the number of hits on a Web site link 
A) the outcomes of rolling two dice 
B) the time to complete a specific task 
C) the number of new hires in a year 
D) the number of hits on a Web site link

Question 10

The expected value and variance of the Poisson distribution are equal to λ.

Accepted Answer

A) True 
 B)False

Question 11

The ________ of a random variable corresponds to the notion of the mean, or average, for a sample.

Accepted Answer

A) mode 
B) variance 
C) expected value 
D) standard deviation 
A) mode 
B) variance 
C) expected value 
D) standard deviation

Question 12

Identify the correct statement from the following.

Accepted Answer

A) The events that a respondent is female and chooses Math are not independent. 
B) All events are independent of each other. 
C) The events that a respondent is male and chooses Science are not dependent. 
D) The events that a respondent is female and that she chooses Science are independent. 
A) The events that a respondent is female and chooses Math are not independent. 
B) All events are independent of each other. 
C) The events that a respondent is male and chooses Science are not dependent. 
D) The events that a respondent is female and that she chooses Science are independent.

Question 13

Which of the following is true of normal distributions?

Accepted Answer

A) The mean, median, and mode are all equal. 
B) Its measure of skewness is always greater than 1. 
C) The range of the random variable X is bounded. 
D) Mathematical formulas make it easier to compute normal distributions. 
A) The mean, median, and mode are all equal. 
B) Its measure of skewness is always greater than 1. 
C) The range of the random variable X is bounded. 
D) Mathematical formulas make it easier to compute normal distributions.

Question 14

Use the data given below to answer the following question(s).
In an event $ X $, the probability of rolling a sum of 8 on two dice is $ \frac{5}{36} $ while the probability of rolling an 11 is $ \frac{2}{36} $. In another event $ Y $, the probability of rolling a 2 is $ \frac{1}{36} $, the probability of rolling a 9 is $ \frac{4}{36} $, and the probability of rolling a 4 is $ \frac{3}{36} $. 
-What is the probability that either event X or Y occurs?

Accepted Answer

A) $\frac{8}{36}$ 
B) $\frac{15}{36}$ 
C) $\frac{7}{36}$ 
D) $\frac{1}{36}$ 
A) $\frac{8}{36}$ 
B) $\frac{15}{36}$ 
C) $\frac{7}{36}$ 
D) $\frac{1}{36}$

Question 15

Use the data given below to answer the following question(s).
On an average, the number of students that choose to study Arts subjects at Greyin Tide University is 17 each year.(Hint: Use Poisson distribution formula).
-What is the probability of 8 takers or less for Arts subjects in the coming year?

Accepted Answer

A) 0.00716 
B) 0.01316 
C) 0.03164 
D) 0.04744 
A) 0.00716 
B) 0.01316 
C) 0.03164 
D) 0.04744

Question 16

Which of the following is the probability mass function of the Bernoulli distribution?

Accepted Answer

A) $\left\{\begin{aligned}
p & \text { if } x=1 \
1-p & \text { if } x=0
\end{aligned}\right.$ 
B) 
  
C) $\frac{n !}{x !(n-x) !}$ 
D) 
$\left\{ \begin{array} { c } 
\frac { e ^ { - \lambda } \lambda ^ { x } } { x ! } , \
0 , \quad \text { otherwise }
\end{array} \text { for } x = 0,1,2 , \ldots \right.$ 
A) $\left\{\begin{aligned}
p & \text { if } x=1 \
1-p & \text { if } x=0
\end{aligned}\right.$ 
B) 
  
C) $\frac{n !}{x !(n-x) !}$ 
D) 
$\left\{ \begin{array} { c } 
\frac { e ^ { - \lambda } \lambda ^ { x } } { x ! } , \
0 , \quad \text { otherwise }
\end{array} \text { for } x = 0,1,2 , \ldots \right.$

Question 17

Which of the following is true about probability density functions?

Accepted Answer

A) A graph of the density function must lie at or below the x-axis. 
B) The total area under the density function below the x-axis is 2.0. 
C) It calculates the probability of a random variable lying between a certain interval. 
D) P (a)x P (b)is the area under the density function between two numbers a and b. 
A) A graph of the density function must lie at or below the x-axis. 
B) The total area under the density function below the x-axis is 2.0. 
C) It calculates the probability of a random variable lying between a certain interval. 
D) P (a)x P (b)is the area under the density function between two numbers a and b.

Question 18

Which of the following is true of the parameters of a beta distribution function?

Accepted Answer

A) The parameters of the distribution function, α and β, can be negative. 
B) The values of the parameters do not affect the skewness of the distribution. 
C) If either parameter is 1.0 and the other is lesser than 1.0, the distribution takes an "L" shape. 
D) If the parameter β exceeds the other parameter α, the distribution is positively skewed. 
A) The parameters of the distribution function, α and β, can be negative. 
B) The values of the parameters do not affect the skewness of the distribution. 
C) If either parameter is 1.0 and the other is lesser than 1.0, the distribution takes an "L" shape. 
D) If the parameter β exceeds the other parameter α, the distribution is positively skewed.

Question 19

Which of the following is a weighted average of the squared deviations from the expected value?

Accepted Answer

A) skewness 
B) mean difference 
C) kurtosis 
D) variance 
A) skewness 
B) mean difference 
C) kurtosis 
D) variance

Question 20

Use the data given below to answer the following question(s).
In an event $ X $, the probability of rolling a sum of 8 on two dice is $ \frac{5}{36} $ while the probability of rolling an 11 is $ \frac{2}{36} $. In another event $ Y $, the probability of rolling a 2 is $ \frac{1}{36} $, the probability of rolling a 9 is $ \frac{4}{36} $, and the probability of rolling a 4 is $ \frac{3}{36} $. 
-Which of the following computes the probability of an event P given that event Q is known to have occurred?

Accepted Answer

The Excel function NORM.DIST finds probabilities for the standard normal distribution.

What are the properties of a probability mass function?

Which of the following is true about using sample data?

The exponential distribution:

Which of the following will hold true if events X and Y are independent?

Which of the following characterizes a random variable having two possible outcomes, each with a constant probability of occurrence?

Which of the following is true about the classical definition of probability?

Which of the following is a continuous random variable?

The expected value and variance of the Poisson distribution are equal to λ.

The ________ of a random variable corresponds to the notion of the mean, or average, for a sample.

Identify the correct statement from the following.

Which of the following is true of normal distributions?

Which of the following is the probability mass function of the Bernoulli distribution?

Which of the following is true about probability density functions?

Which of the following is true of the parameters of a beta distribution function?

Which of the following is a weighted average of the squared deviations from the expected value?

Introduction to Business Analytics

Analytics on Spreadsheets

Visualizing and Exploring Data

Descriptive Statistical Measures

Sampling and Estimation

Statistical Inference

Predictive Modeling and Analysis

Regression Analysis

Forecasting Techniques

Simulation and Risk Analysis

Introduction to Data Mining

Linear Optimization

Applications of Linear Optimization

Integer Optimization

Nonlinear and Non-Smooth Optimization

Optimization Models with Uncertainty

Decision Analysis

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Exam 5: Probability Distributions and Data Modeling

The Excel function NORM.DIST finds probabilities for the standard normal distribution.

What are the properties of a probability mass function?

Which of the following is true about using sample data?

The exponential distribution:

Which of the following will hold true if events X and Y are independent?

Which of the following characterizes a random variable having two possible outcomes, each with a constant probability of occurrence?

Which of the following is true about the classical definition of probability?

Which of the following is a continuous random variable?

The expected value and variance of the Poisson distribution are equal to λ.

The ________ of a random variable corresponds to the notion of the mean, or average, for a sample.

Identify the correct statement from the following.

Which of the following is true of normal distributions?

Which of the following is the probability mass function of the Bernoulli distribution?

Which of the following is true about probability density functions?

Which of the following is true of the parameters of a beta distribution function?

Which of the following is a weighted average of the squared deviations from the expected value?

Introduction to Business Analytics

Analytics on Spreadsheets

Visualizing and Exploring Data

Descriptive Statistical Measures

Sampling and Estimation

Statistical Inference

Predictive Modeling and Analysis

Regression Analysis

Forecasting Techniques

Simulation and Risk Analysis

Introduction to Data Mining

Linear Optimization

Applications of Linear Optimization

Integer Optimization

Nonlinear and Non-Smooth Optimization

Optimization Models with Uncertainty

Decision Analysis

Filters