Question 1

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The continuous random variable X is uniformly distributed over the interval 4 to 10.
-What is the standard deviation of this distribution?
A)1.732
B)3.162
C)2.646
D)2.449

Accepted Answer

The standard deviation of a uniform distribution is given by the formula σ = (b - a) / √12, where a and b are the lower and upper bounds of the distribution, respectively. In this case, a = 4 and b = 10, so σ = (10 - 4) / √12 = 6 / √12 = 1.732.

Question 2

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The continuous random variable X is uniformly distributed over the interval 4 to 10.
-What is P(5 ≤ X ≤ 11)?
A)0.167
B)0.833
C)1.000
D)0.000

Accepted Answer

To find P(5 ≤ X ≤ 11), we first need to determine the range of X. Since X is uniformly distributed over the interval 4 to 10, its range is 10 - 4 = 6.

Next, we need to determine the probability that X falls within the given range. This can be done using the formula for the uniform distribution:

P(a ≤ X ≤ b) = (b - a) / (max - min)

Where a and b are the endpoints of the range of interest, and max and min are the maximum and minimum possible values of X.

In our case, a = 5, b = 10 (since X cannot exceed 10), max = 10, and min = 4. Substituting these values into the formula, we get:

P(5 ≤ X ≤ 10) = (10 - 5) / (10 - 4) = 5 / 6 ≈ 0.833

Therefore, the answer is B.

Question 3

The cumulative distribution function can be illustrated by using a simple probability structure.

Accepted Answer

The cumulative distribution function (CDF) is a function that maps the possible values of a random variable to their cumulative probability. It can be illustrated using a simple probability structure, such as a coin toss or rolling a die, where the possible outcomes are discrete and finite. Therefore, the statement is true.

Question 4

The term used by fund managers to describe the relationships between two stock prices is:
A)speculating.
B)hedging.
C)investing.
D)betting.

Accepted Answer

Hedging refers to the practice of investing in two stocks that function in opposing ways. This allows fund managers to reduce risk and ensure some degree of stability within their portfolio. Speculating, investing, and betting do not accurately describe the relationships between two stock prices.

Question 5

The probability that a random variable lies between a pair of values is the area under the probability density function to the left of the two values.

Accepted Answer

The probability that a random variable lies between a pair of values is actually the area under the probability density function between those two values, not just to the left of them.

Question 6

If Z is a standard normal random variable,then P(-1.25 ≤ Z ≤ -0.75)is:
A)0.6678
B)0.1056
C)0.2266
D)0.1210

Accepted Answer

The answer of If Z is a standard normal random...

Question 7

The normal distribution is an example of a(n):
A)discrete distribution.
B)continuous distribution.
C)binomial distribution.
D)exponential distribution.

Accepted Answer

The normal distribution is a continuous distribution, as it represents a probability density curve that can take on any value within a range of values. Discrete distributions, like the binomial distribution, only take on specific values, while the exponential distribution describes the probability of waiting for a certain amount of time before an event occurs.

Question 8

A continuous uniform random variable has a constant probability density function everywhere within the range of values the random variable can take.

Accepted Answer

This is the definition of a continuous uniform random variable.

Question 9

The area to the left of the mean in any normal distribution is equal to:
A)the median.
B)the standard deviation.
C)1.0
D)0.5

Accepted Answer

The area to the left of the mean in any normal distribution is equal to 0.5 or 50%. This is because the distribution is symmetrical around the mean, with 50% of the area on each side of the mean. Therefore, the correct choice is D) 0.5.

Question 10

The distribution that has been found to be particularly useful for waiting-line or queuing problems is referred to as the:
A)exponential distribution.
B)hypergeometric distribution.
C)marginal distribution.
D)standard normal distribution.

Accepted Answer

The exponential distribution is particularly useful for waiting-line or queuing problems because it models the time between arrivals or service completions in a system. It is often used to analyze waiting times in customer service, transportation systems, and manufacturing processes. The other distributions listed do not have a direct relationship to waiting-line or queuing problems.

Question 11

Given that Z is a standard normal variable,the value z₁ for which P(Z ≤ z₁)= 0.242 is: A)0.70 B)0.65 C)-0.70 D)-0.65

Accepted Answer

The value of $z_{0.242}$ is negative because 0.242 is less than 0.5, which corresponds to the left side of the standard normal distribution curve. The correct value is approximately -0.70.

Question 12

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The continuous random variable X is uniformly distributed over the interval 4 to 10.
-What is the mean of this distribution?
A)4
B)5
C)6
D)7

Accepted Answer

The mean of a uniform distribution is calculated as (a + b) / 2, where a and b are the minimum and maximum values of the distribution, respectively. Here, a = 4 and b = 10, so the mean is (4 + 10) / 2 = 7.

Question 13

Many economic and business measures such as sales,investment,consumption,costs,and revenues can be represented by continuous random variables.

Accepted Answer

Yes, economic and business measures such as sales, investment, consumption, costs, and revenues can indeed be represented by continuous random variables since they can take on any value within a certain range or interval. Examples could include the amount of money spent on a certain product, the income generated by a particular industry, or the cost of production for a company. These variables can often be modeled using probability distributions such as the normal distribution, the exponential distribution, or the uniform distribution.

Question 14

One must use caution concerning finance models in that continuous clear observation and thinking cannot be replaced by models developed from:
A)foreign markets.
B)futures.
C)past events.
D)human error.

Accepted Answer

Finance models developed solely from past events may not accurately predict future financial trends and thus, cannot replace continuous clear observation and thinking. While foreign markets and futures may also be unreliable predictors, human error is not mentioned as a factor in the statement.

Question 15

The combinations of continuous random variables whose development is based on operation with expected values and does not depend on the particular probability distribution are called:
A)marginal combinations.
B)frequent combinations.
C)linear combinations.
D)disjointed combinations.

Accepted Answer

Combinations of continuous random variables that are based on expected values and are not dependent on the particular probability distribution are known as linear combinations. Marginal combinations do not involve expected values, frequent combinations are not a recognized term, and disjointed combinations do not involve expected values or combinations of random variables.

Question 16

Which type of random variables are used to model market values of various stock prices,production and sales patterns,and studies of import and export behavior?
A)consistent
B)marginal
C)hypergeometric
D)jointly distributed

Accepted Answer

Jointly distributed random variables are used to model market values of various stock prices, production and sales patterns, and studies of import and export behavior. This is because these types of variables are used to model the behavior of multiple variables simultaneously.

Question 17

The mean of a probability distribution provides a measure of the center of the distribution.

Accepted Answer

The mean is calculated as the sum of all possible outcomes multiplied by their probabilities, and it represents the average or expected value of the distribution. Therefore, it is a measure of the center of the distribution.

Question 18

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The continuous random variable X is uniformly distributed over the interval 4 to 10.
-What is P(6 ≤ X ≤ 8)?
A)0.167
B)0.333
C)0.567
D)0.833

Accepted Answer

Since X is uniformly distributed, the probability of any value in the interval 4 to 10 is equally likely. The total length of the interval is 10-4=6, and the length of the subinterval 6 ≤ X ≤ 8 is 8-6=2. Therefore, the probability of X being in the subinterval 6 ≤ X ≤ 8 is equal to the length of the subinterval divided by the total length of the interval, which is 2/6 or 1/3, so the answer is B.

Question 19

The variance of a probability distribution provides a measure of the average spread of a distribution.

Accepted Answer

The answer of The variance of a probability distribution provides...

Question 20

Suppose X is a normal random variable with mean of 70 and standard deviation of 4.The Z-score was calculated for a number,and it was 2.85.What is X?
A)58.6
B)81.4
C)65.8
D)75.7

Accepted Answer

The Z-score formula is Z = (X - μ) / σ, where Z is the Z-score, X is the value in question, μ is the mean, and σ is the standard deviation. Plugging in the values: 2.85 = (X - 70) / 4. Solving for X gives X = 2.85 * 4 + 70 = 81.4.

Quiz 5: Continuous Random Variables and Probability Distributions

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The continuous random variable X is uniformly distributed over the interval 4 to 10. -What is the standard deviation of this distribution?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The continuous random variable X is uniformly distributed over the interval 4 to 10. -What is P(5 ≤ X ≤ 11) ?

The cumulative distribution function can be illustrated by using a simple probability structure.

The term used by fund managers to describe the relationships between two stock prices is:

The probability that a random variable lies between a pair of values is the area under the probability density function to the left of the two values.

If Z is a standard normal random variable,then P(-1.25 ≤ Z ≤ -0.75) is:

The normal distribution is an example of a(n) :

A continuous uniform random variable has a constant probability density function everywhere within the range of values the random variable can take.

The area to the left of the mean in any normal distribution is equal to:

The distribution that has been found to be particularly useful for waiting-line or queuing problems is referred to as the:

Given that Z is a standard normal variable,the value z₁ for which P(Z ≤ z₁) = 0.242 is:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The continuous random variable X is uniformly distributed over the interval 4 to 10. -What is the mean of this distribution?

Many economic and business measures such as sales,investment,consumption,costs,and revenues can be represented by continuous random variables.

One must use caution concerning finance models in that continuous clear observation and thinking cannot be replaced by models developed from:

The combinations of continuous random variables whose development is based on operation with expected values and does not depend on the particular probability distribution are called:

Which type of random variables are used to model market values of various stock prices,production and sales patterns,and studies of import and export behavior?

The mean of a probability distribution provides a measure of the center of the distribution.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The continuous random variable X is uniformly distributed over the interval 4 to 10. -What is P(6 ≤ X ≤ 8) ?

The variance of a probability distribution provides a measure of the average spread of a distribution.

Suppose X is a normal random variable with mean of 70 and standard deviation of 4.The Z-score was calculated for a number,and it was 2.85.What is X?

Quiz 5: Continuous Random Variables and Probability Distributions

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The continuous random variable X is uniformly distributed over the interval 4 to 10. -What is the standard deviation of this distribution?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The continuous random variable X is uniformly distributed over the interval 4 to 10. -What is P(5 ≤ X ≤ 11) ?

The cumulative distribution function can be illustrated by using a simple probability structure.

The term used by fund managers to describe the relationships between two stock prices is:

The probability that a random variable lies between a pair of values is the area under the probability density function to the left of the two values.

If Z is a standard normal random variable,then P(-1.25 ≤ Z ≤ -0.75) is:

The normal distribution is an example of a(n) :

A continuous uniform random variable has a constant probability density function everywhere within the range of values the random variable can take.

The area to the left of the mean in any normal distribution is equal to:

The distribution that has been found to be particularly useful for waiting-line or queuing problems is referred to as the:

Given that Z is a standard normal variable,the value z1 for which P(Z ≤ z1) = 0.242 is:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The continuous random variable X is uniformly distributed over the interval 4 to 10. -What is the mean of this distribution?

Many economic and business measures such as sales,investment,consumption,costs,and revenues can be represented by continuous random variables.

One must use caution concerning finance models in that continuous clear observation and thinking cannot be replaced by models developed from:

The combinations of continuous random variables whose development is based on operation with expected values and does not depend on the particular probability distribution are called:

Which type of random variables are used to model market values of various stock prices,production and sales patterns,and studies of import and export behavior?

The mean of a probability distribution provides a measure of the center of the distribution.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The continuous random variable X is uniformly distributed over the interval 4 to 10. -What is P(6 ≤ X ≤ 8) ?

The variance of a probability distribution provides a measure of the average spread of a distribution.

Suppose X is a normal random variable with mean of 70 and standard deviation of 4.The Z-score was calculated for a number,and it was 2.85.What is X?

Given that Z is a standard normal variable,the value z₁ for which P(Z ≤ z₁) = 0.242 is: