Deck 5: Probability Distributions and Data Modeling

Question 1

Explain the characteristics and applications of discrete probability distributions 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 that exactly 13 students will take up Arts in the coming year?

A) 0.08795
B) 0.20087
C) 0.04798
D) 0.06585

Answer 1

D

Question 2

Identify and apply the basic concepts and tools of probability Use the data given below to answer the following question(s).
At a casino, a combination of two spinners is used to decide the winner based on the sum of scores from spinning. The spinners each have four colored spaces - red, yellow, blue, and green. Red = 1, Yellow = 2, Blue = 3, and Green = 4
Compute the variance of the random variable that denotes the possible summed scores from the two spinners.

Answer 2

The variance, Var[X], of a discrete random variable X as a weighted average of the squared deviations from the expected value:

Question 3

The Kolmogorov-Smirnov procedure:

A) compares the cumulative distribution of the data with the theoretical distribution to base its conclusion.
B) puts more weight on the differences between the tails of the distributions.
C) breaks down the theoretical distribution into areas of equal probability and compares the data points within each area to the number that would be expected for that distribution.
D) is useful when a better fit is needed at the extreme tails of the distribution.

Answer 3

A

Question 4

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

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 5

Which of the following characterizes a continuous random variable for which all outcomes between some minimum and maximum value are equally likely?

A) exponential distribution
B) uniform distribution
C) normal distribution
D) lognormal distribution

Question 6

Identify and apply the basic concepts and tools of probability Use the data given below to answer the following question(s).
At a casino, a combination of two spinners is used to decide the winner based on the sum of scores from spinning. The spinners each have four colored spaces - red, yellow, blue, and green. Red = 1, Yellow = 2, Blue = 3, and Green = 4
Compute the expected value of the random variable that denotes the possible summed scores from the
two spinners.

Question 7

Which of the following is true of 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 8

Explain the characteristics and applications of discrete probability distributions Use the data given below to answer the following question(s).
The profit from selling folding tables varies uniformly each quarter between $1,500 and $2,300.
What is the probability that profit will be less than $1,900?

Question 9

Which of the following is true about probability density functions?

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 within a certain interval.
D) P (a) x P (b) is the area under the density function between two numbers a and b.

Question 10

A probability density function:

A) is the probability distribution of discrete outcomes.
B) suggests that the probability that a random variable assumes a specific value must be positive.
C) characterizes outcomes of a continuous random variable.
D) can yield negative values depending on the values of the random variable, X.

Question 11

Identify and apply the basic concepts and tools of probability Use the data given below to answer the following question(s).
At a casino, a combination of two spinners is used to decide the winner based on the sum of scores from spinning. The spinners each have four colored spaces - red, yellow, blue, and green. Red = 1, Yellow = 2, Blue = 3, and Green = 4
What is the probability that the spinners land on colors summing up to exactly 3?

Question 12

Which of the following distributions is appropriate when the probability of zero is very low, but the most likely value is just greater than zero?

A) triangular distribution
B) exponential distribution
C) lognormal distribution
D) beta distribution

Question 13

The exponential distribution:

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 14

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

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 15

Which of the following is true about using sample data?

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.

Question 16

John and Mike were offered mints. What is the probability that at least John or Mike would respond favorably? (Hint: Use the classical definition).

Question 17

Which of the following is true about the Random Number Generation tool?

A) The Random Number Generation dialog presents only three distributions to choose from: beta, lognormal, and triangular.
B) The default distribution in this tool is the continuous distribution.
C) Repeating the process generates a new set of sample values.
D) Pressing the recalculation (F9) key is an easy way to change the values generated.

Question 18

Explain the characteristics and applications of discrete probability distributions 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?

A) 0.00716
B) 0.01260
C) 0.03164
D) 0.04744

Question 19

Explain the characteristics and applications of discrete probability distributions Use the data given below to answer the following question(s).
The profit from selling folding tables varies uniformly each quarter between $1,500 and $2,300.
What is the probability that profit will be between $2,000 and $2,200?

Question 20

Consider an event X comprised of three outcomes whose probabilities are Compute the probability of the complement of the event.

Question 21

The VLOOKUP function in Excel can be used to generate outcomes from any discrete distribution.

Question 22

If P(X|Y) = P(X), it implies that event Y is dependent on event X.

Question 23

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

Question 24

How are probability, experiment, outcome, and sample space related to each other?

Question 25

What is a random number? How is it generated in Excel?

Question 26

What are the properties of a probability mass function?

Question 27

Explain the similarity between the formulas for computing population mean and expected value of discrete random variable X.

Question 28

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

Question 29

How can normal probabilities be computed using Excel? Given the cumulative probability, how can the value of the random variable be found?

Question 30

The beta distribution is a function of three parameters, the minimum, a; maximum, b; and most likely, c.