Question 1

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.
 $\begin{array}{|c|c|c|}
\hline \text { Respondent } & \text { Gender } & \text { Preference } \
\hline 1 & \text { Female } & \text { Art.s } \
\hline 2 & \text { Male } & \text { Science } \
\hline 3 & \text { Male } & \text { Math } \
\hline 4 & \text { Female } & \text { Art.s } \
\hline 5 & \text { Female } & \text { Math } \
\hline 6 & \text { Male } & \text { Science } \
\hline 7 & \text { Male } & \text { Math } \
\hline 8 & \text { Male } & \text { Math } \
\hline 9 & \text { Female } & \text { Art.s } \
\hline 10 & \text { Male } & \text { Art.s } \
\hline 11 & \text { Male } & \text { Science } \
\hline 12 & \text { Female } & \text { Science } \
\hline 13 & \text { Female } & \text { Math } \
\hline 14 & \text { Male } & \text { Art.s } \
\hline 15 & \text { Female } & \text { Art.s }
\end{array}$
-Use the multiplication law of probability to compute the probability that the respondent is male and prefers Math.

Accepted Answer

A) $\frac{8}{75}$ 
B) $\frac{3}{8}$ 
C) $\frac{3}{225}$ 
D) $\frac{3}{15}$

Question 2

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} $. 
-Consider an event Z that includes all outcomes of rolling two dice whose sum is odd.What is the probability that either event Y or Z occurs?

Accepted Answer

A) $\frac{26}{36}$ 
B) $\frac{22}{36}$ 
C) $\frac{10}{36}$ 
D) $\frac{18}{36}$

Question 3

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?

Accepted Answer

A) 0.08795 
B) 0.20087 
C) 0.04798 
D) 0.06579

Question 4

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?

Accepted Answer

The answer of Use the data given below to answer...

Question 5

While rolling two dice, what is the probability of rolling a sum of 7 or more?

Accepted Answer

A)  $\frac{7}{12}$ 
B)  $\frac{5}{9}$ 
C)  $\frac{1}{6}$ 
D)  $\frac{5}{36}$

Question 6

For a discrete random variable X, which of the following computes the expected value?

Accepted Answer

A)  $\sum f\left(x_{i}\right)$ 
B)  $\sum_{i=1}^{\infty} x_{i} f\left(x_{i}\right)$ 
C)  $\sum_{i=1}^{\infty} x_{i}$ 
D)  $\sum \frac { f ( x ) } { x }$

Question 7

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

Accepted Answer

A)   $\frac{1}{8}$ 
B)  $\frac{3}{4}$ 
C) $\frac{1}{8}$ . 
D) $\frac{3}{8}$ ,

Question 8

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

Accepted Answer

The answer of How are probability, experiment, outcome, and sample...

Question 9

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 probability that neither X nor Y will occur?

Accepted Answer

A) $\frac{29}{26}$ 
B) $\frac{1}{36}$ 
C) $\frac{28}{36}$ 
D) $\frac{21}{36}$

Question 10

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

Accepted Answer

The answer of What is a random number? How is...

Question 11

The binominal distribution:

Accepted Answer

A) is a discrete distribution used to model the number of occurrences in some unit of measure. 
B) assumes that the average number of occurrences per unit is a constant and that occurrences are independent. 
C) is symmetric irrespective of the value of the probability of success. 
D) models n independent replications of a Bernoulli experiment, each with a probability p of success.

Question 12

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

Accepted Answer

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 13

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?

Accepted Answer

The answer of Use the data given below to answer...

Question 14

Which of the following is true about variance?

Accepted Answer

A) It measures the uncertainty of a random variable. 
B) Higher variance implies low uncertainty. 
C) It is the square root of a random variable's standard deviation. 
D) It is the weighted average of all possible outcomes.

Question 15

The Kolmogorov-Smirnov procedure:

Accepted Answer

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.

Question 16

Which of the following is true of the binomial distribution?

Accepted Answer

A) The expected value of the binomial distribution is np (1 - p), where n is the number of experiments and p is the probability of success. 
B) The binomial distribution can assume different shapes and amounts of skewness, depending on the parameters. 
C) In Excel's binomial distribution function, setting cumulative to TRUE will provide the probability mass function for a specified value. 
D) The expected value of the binomial distribution is λ, a constant.

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

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.

Accepted Answer

The answer of Use the data given below to answer...

Question 19

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?

Accepted Answer

The answer of Use the data given below to answer...

Question 20

Consider an event X comprised of three outcomes whose probabilities are $\frac{9}{18}, \frac{1}{18}, \text { and } \frac{6}{18}$ Compute the probability of the complement of the event.

Accepted Answer

A)  $\frac{2}{18}$ 
B) $\frac{1}{2}$ 
C) $\frac{16}{3}$ 
D) $\frac{16}{18}$.

Exam 5: Probability Distributions and Data Modeling

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?

While rolling two dice, what is the probability of rolling a sum of 7 or more?

For a discrete random variable X, which of the following computes the expected value?

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

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

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

The binominal distribution:

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

Which of the following is true about variance?

The Kolmogorov-Smirnov procedure:

Which of the following is true of the binomial distribution?

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

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?

Consider an event X comprised of three outcomes whose probabilities are $\frac{9}{18}, \frac{1}{18}, \text { and } \frac{6}{18}$ Compute the probability of the complement of the event.

Exam 5: Probability Distributions and Data Modeling

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?

While rolling two dice, what is the probability of rolling a sum of 7 or more?

For a discrete random variable X, which of the following computes the expected value?

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

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

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

The binominal distribution:

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

Which of the following is true about variance?

The Kolmogorov-Smirnov procedure:

Which of the following is true of the binomial distribution?

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

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?

Consider an event X comprised of three outcomes whose probabilities are 918,118, and 618\frac{9}{18}, \frac{1}{18}, \text { and } \frac{6}{18}189​,181​, and 186​ Compute the probability of the complement of the event.

Consider an event X comprised of three outcomes whose probabilities are $\frac{9}{18}, \frac{1}{18}, \text { and } \frac{6}{18}$ Compute the probability of the complement of the event.