Question 1

Which of the following statements is correct?

Accepted Answer

A) The binomial and normal distributions are both discrete probability distributions. 
B) The binomial and normal distributions are both continuous probability distributions. 
C) The binomial distribution is a continuous probability distribution and the normal distribution is a discrete probability distribution. 
D) The binomial distribution is a discrete probability distribution and the normal distribution is a continuous probability distribution. 
A) The binomial and normal distributions are both discrete probability distributions. 
B) The binomial and normal distributions are both continuous probability distributions. 
C) The binomial distribution is a continuous probability distribution and the normal distribution is a discrete probability distribution. 
D) The binomial distribution is a discrete probability distribution and the normal distribution is a continuous probability distribution.

Question 2

A nickel and a dime are tossed. How many possible outcomes are in this event?​

Accepted Answer

There are

Question 3

Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability density function for the time it takes to fill an order? ??

Accepted Answer

A)  $f ( x ) = \frac { 1 } { 5 } e ^ { - \frac { x } { 5 } }$ 
B) ? $f ( x ) = \frac { 1 } { 3 } e ^ { - \frac { x } { 3 } }$ 
C) ? $f ( x ) = \frac { 2 } { 3 } e ^ { - \frac { 2 } { 3 } x }$ 
D) None of the above answers are correct. 
A)  $f ( x ) = \frac { 1 } { 5 } e ^ { - \frac { x } { 5 } }$ 
B) ? $f ( x ) = \frac { 1 } { 3 } e ^ { - \frac { x } { 3 } }$ 
C) ? $f ( x ) = \frac { 2 } { 3 } e ^ { - \frac { 2 } { 3 } x }$ 
D) None of the above answers are correct.

Question 4

Given that P(A) = 0.3, P(A|B) = 0.4, and P(B) = 0.5, compute P(A ∩ B)

Accepted Answer

The answer of Given that P(A) = 0.3, P(A|B) =...

Question 5

James has two fair coins. When he flips them, what is the sample space?

Accepted Answer

heads-heads, heads-t

Question 6

A bucket contains 2 red balls, 4 yellow balls, and 5 purple balls. One ball is taken from the bucket and then replaced. Another ball is taken from the bucket. What is the probability that the first ball is red and the second ball is purple?

Accepted Answer

The answer of A bucket contains 2 red balls, 4...

Question 7

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. What percent of the time does he exceed 13,000 steps?

Accepted Answer

A) 2.28% 
B) 5.0% 
C) 95% 
D) 97.72% 
A) 2.28% 
B) 5.0% 
C) 95% 
D) 97.72%

Question 8

The random variable X is known to be uniformly distributed between 2 and 12. Compute P(X > 10).
​

Accepted Answer

The answer of The random variable X is known to...

Question 9

Let X be a random variable with a Uniform distribution between 8 and 20. Find the probability that X is less than 10?
​

Accepted Answer

The answer of Let X be a random variable with...

Question 10

You recently took a standardized test in which scores follow a normal distribution with a mean of 18 and a standard deviation of 3. You were told that your score is at the 75th percentile of this distribution. What is your score?
​
​

Accepted Answer

Question 11

The center of a normal curve is

Accepted Answer

A) always equal to zero. 
B) the mean of the distribution. 
C) always a positive number. 
D) equal to the standard deviation. 
A) always equal to zero. 
B) the mean of the distribution. 
C) always a positive number. 
D) equal to the standard deviation.

Question 12

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. One day he took 15,000 steps. What was his percentile on that day? ​​

Accepted Answer

A) 95% 
B) 97.7% 
C) 99.7% 
D) 100% 
A) 95% 
B) 97.7% 
C) 99.7% 
D) 100%

Question 13

Which of the following is not a characteristic of the normal probability distribution?

Accepted Answer

A) The mean, median, and the mode are equal. 
B) The mean of the distribution can be negative, zero, or positive. 
C) The distribution is symmetrical. 
D) The standard deviation must be 1. 
A) The mean, median, and the mode are equal. 
B) The mean of the distribution can be negative, zero, or positive. 
C) The distribution is symmetrical. 
D) The standard deviation must be 1.

Question 14

Participants at the state fair were given 8 rings to toss. The number x of rings tossed onto a stick can be approximated by the probability distribution in the table. Use the probability distribution to find the mean and variance of the probability distribution.
​ $$\begin{array} { | l | c | } 
\hline x & f ( x ) \
\hline 0 & 0.010 \
\hline 1 & 0.030 \
\hline 2 & 0.070 \
\hline 3 & 0.070 \
\hline 4 & 0.100 \
\hline 5 & 0.210 \
\hline 6 & 0.320 \
\hline 7 & 0.130 \
\hline 8 & 0.060 \
\hline
\end{array}$$ ​
​

Accepted Answer

The answer of Participants at the state fair were given...

Question 15

The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What is the probability that, if driven normally, the car will get 100 miles per gallon or better? ​​

Accepted Answer

A) 0.6% 
B) 2.5% 
C) 6% 
D) 25% 
A) 0.6% 
B) 2.5% 
C) 6% 
D) 25%

Question 16

The contingency table below represents employees of a communications company classified by age and field of expertise. Fill in the missing entries.
​ $$\begin{array} { | l | c | c | c | c | } 
\hline & \text { Under } \mathbf { 3 5 } & \mathbf { 3 5 } - \mathbf { 4 4 } & \mathbf { 4 5 } + & \text { Total } \
\hline \text { Engineering } & 7,635 & 7,875 & 6,429 & \mathbf { 2 1 , 9 3 9 } \
\hline \text { Business } & 13,195 & & & \mathbf { 3 8 , 8 1 4 } \
\hline \text { Education } & 4,802 & 5,143 & & \
\hline \text { Liberal Arts } & 10,377 & 10,440 & 11,010 & 31,827 \
\hline { \text { Total } } & \mathbf { 3 6 , 0 0 9 } & & \mathbf { 3 7 , 3 1 3 } & \mathbf { 1 1 0 , 4 0 5 } \
\hline
\end{array}$$ ​

Accepted Answer

@#IMG-DLM& ​
110,405 - (36,009 + 37,313)

Question 17

Sample space is

Accepted Answer

A) ​a process that results in some outcome. 
B) ​the collection of all possible outcomes. 
C) the collection of events 
D) ​a subgroup of a population/the likelihood of an outcome. 
A) ​a process that results in some outcome. 
B) ​the collection of all possible outcomes. 
C) the collection of events 
D) ​a subgroup of a population/the likelihood of an outcome.

Question 18

What type of distribution models the number of occurrences of an event over a specified interval of time or space?
​

Accepted Answer

A Poisson

Question 19

Reviews of call center representatives over the last 3 years showed that 10% of all call center representatives were rated as outstanding, 75% were rated as excellent/good, 10% percent were rated as satisfactory, and 5% were considered unsatisfactory. For a sample of 10 reps selected at random, what is the probability that two will be rated as unsatisfactory?
​
​

Accepted Answer

The answer of Reviews of call center representatives over the...

Question 20

The random variable X is known to be uniformly distributed between 2 and 12. Compute P(X = 3).
​

Accepted Answer

The answer of The random variable X is known to...

Which of the following statements is correct?

A nickel and a dime are tossed. How many possible outcomes are in this event?

Given that P(A) = 0.3, P(A|B) = 0.4, and P(B) = 0.5, compute P(A ∩ B)

James has two fair coins. When he flips them, what is the sample space?

A bucket contains 2 red balls, 4 yellow balls, and 5 purple balls. One ball is taken from the bucket and then replaced. Another ball is taken from the bucket. What is the probability that the first ball is red and the second ball is purple?

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. What percent of the time does he exceed 13,000 steps?

The random variable X is known to be uniformly distributed between 2 and 12. Compute P(X > 10).

Let X be a random variable with a Uniform distribution between 8 and 20. Find the probability that X is less than 10?

You recently took a standardized test in which scores follow a normal distribution with a mean of 18 and a standard deviation of 3. You were told that your score is at the 75^th percentile of this distribution. What is your score?

The center of a normal curve is

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. One day he took 15,000 steps. What was his percentile on that day?

Which of the following is not a characteristic of the normal probability distribution?

The contingency table below represents employees of a communications company classified by age and field of expertise. Fill in the missing entries. Under - + Total Engineering 7,635 7,875 6,429 Business 13,195 Education 4,802 5,143 Liberal Arts 10,377 10,440 11,010 31,827 Total

Sample space is

What type of distribution models the number of occurrences of an event over a specified interval of time or space?

The random variable X is known to be uniformly distributed between 2 and 12. Compute P(X = 3).

Introduction

Descriptive Statistics

Data Visualization

Descriptive Data Mining

Statistical Inference

Linear Regression

Time Series Analysis and Forecasting

Predictive Data Mining

Spreadsheet Models

Linear Optimization Models

Integer Linear Optimization Models

Nonlinear Optimization Models

Monte Carlo Simulation

Decision Analysis

Filters

Exam 5: Probability: an Introduction to Modeling Uncertainty

Which of the following statements is correct?

A nickel and a dime are tossed. How many possible outcomes are in this event?​

Given that P(A) = 0.3, P(A|B) = 0.4, and P(B) = 0.5, compute P(A ∩ B)

James has two fair coins. When he flips them, what is the sample space?

A bucket contains 2 red balls, 4 yellow balls, and 5 purple balls. One ball is taken from the bucket and then replaced. Another ball is taken from the bucket. What is the probability that the first ball is red and the second ball is purple?

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. What percent of the time does he exceed 13,000 steps?

The random variable X is known to be uniformly distributed between 2 and 12. Compute P(X > 10). ​

Let X be a random variable with a Uniform distribution between 8 and 20. Find the probability that X is less than 10? ​

You recently took a standardized test in which scores follow a normal distribution with a mean of 18 and a standard deviation of 3. You were told that your score is at the 75th percentile of this distribution. What is your score? ​ ​

The center of a normal curve is

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. One day he took 15,000 steps. What was his percentile on that day? ​​

Which of the following is not a characteristic of the normal probability distribution?

The contingency table below represents employees of a communications company classified by age and field of expertise. Fill in the missing entries. ​ Under - + Total Engineering 7,635 7,875 6,429 Business 13,195 Education 4,802 5,143 Liberal Arts 10,377 10,440 11,010 31,827 Total ​

Sample space is

What type of distribution models the number of occurrences of an event over a specified interval of time or space? ​

The random variable X is known to be uniformly distributed between 2 and 12. Compute P(X = 3). ​

Introduction

Descriptive Statistics

Data Visualization

Descriptive Data Mining

Statistical Inference

Linear Regression

Time Series Analysis and Forecasting

Predictive Data Mining

Spreadsheet Models

Linear Optimization Models

Integer Linear Optimization Models

Nonlinear Optimization Models

Monte Carlo Simulation

Decision Analysis

Filters

A nickel and a dime are tossed. How many possible outcomes are in this event?

The random variable X is known to be uniformly distributed between 2 and 12. Compute P(X > 10).

Let X be a random variable with a Uniform distribution between 8 and 20. Find the probability that X is less than 10?

You recently took a standardized test in which scores follow a normal distribution with a mean of 18 and a standard deviation of 3. You were told that your score is at the 75^th percentile of this distribution. What is your score?

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. One day he took 15,000 steps. What was his percentile on that day?

The contingency table below represents employees of a communications company classified by age and field of expertise. Fill in the missing entries. Under - + Total Engineering 7,635 7,875 6,429 Business 13,195 Education 4,802 5,143 Liberal Arts 10,377 10,440 11,010 31,827 Total

What type of distribution models the number of occurrences of an event over a specified interval of time or space?

The random variable X is known to be uniformly distributed between 2 and 12. Compute P(X = 3).