Question 1

Which of the following best describes a discrete random variable?

Accepted Answer

A variable that has a finite or countable number of possible outcomes.

Question 2

Let $$x$$ represent the number of Fortune 500 companies that lost money in the previous year. Is $$x$$ discrete or continuous, and why?

Accepted Answer

Discrete, because the number of companies can be counted.

Question 3

Which of the following is NOT a requirement for a discrete probability distribution?

Accepted Answer

Each outcome must be equally likely.

Question 4

Given the following probability distribution, determine if it is valid:

$$x$$: 2, 3, 4
$$P(x)$$: 0.5, 0.3, 0.3

Accepted Answer

No, because the sum of the probabilities is greater than 1.

Question 5

A probability distribution is given by $$P(x=1)=0.2$$, $$P(x=2)=0.5$$, $$P(x=3)=0.3. $$What is the mean $$\mu of $$this distribution?

Accepted Answer

$$\mu = 2.1$$

Question 6

Which formula correctly represents the variance $$\$$sigma^2$$ of a discrete probability distribution?

Accepted Answer

$$\$$sigma^2$$ = \sum (x - \mu)^2$ P(x)$$

Question 7

A company surveys 150 employees and records their scores on a test as follows: 24 scored 1, 33 scored 2, 42 scored 3, 30 scored 4, and 21 scored 5. What is the probability that a randomly selected employee scored 4?

Accepted Answer

$$P(x=4) = \frac{30}{150} = 0.20$$

Question 8

If a probability distribution has $$P(x=1)=0.16$$, $$P(x=2)=0.22$$, $$P(x=3)=0.28$$, $$P(x=4)=0.20$$, $$P(x=5)=0.14$$, what is the sum of all probabilities?

Accepted Answer

1.00

Question 9

Which of the following statements about the standard deviation $$\sigma of a $$discrete probability distribution is correct?

Accepted Answer

$$\sigma$$ measures the average distance of the values from the mean.

Question 10

Suppose the mean score $$\mu on a $$test is 2.94 and the variance $$\$$sigma^2$$ is 1.62. What is the standard deviation $$\sigma$$?

Accepted Answer

$$\sigma = 1.27$$

Question 11

A random variable $$x$$ represents the volume of gasoline in a 21-gallon tank. Which type of random variable is $$x$$?

Accepted Answer

Continuous, because the volume can take any value between 0 and 21.

Question 12

Which of the following distributions is NOT a valid probability distribution?

A) $$P(x=1)=0.3$$, $$P(x=2)=0.4$$, $$P(x=3)=0.3
B$$) $$P(x=1)=0.5$$, $$P(x=2)=0.6$$, $$P(x=3)=-0.1
C$$) $$P(x=1)=0.2$$, $$P(x=2)=0.3$$, $$P(x=3)=0.5
D$$) $$P(x=1)=0.1$$, $$P(x=2)=0.2$$, $$P(x=3)=0.7$$

Accepted Answer

B

Question 13

Given a discrete probability distribution with $$\mu = 3$$ and $$\sigma = 2$$, which of the following statements is true?

Accepted Answer

Most values differ from the mean by about 2 units.

Question 14

A histogram of a discrete probability distribution has bars of width 1. What does the area of each bar represent?

Accepted Answer

The probability of the corresponding outcome.

Question 15

If $$P(x=1)=0.16$$, $$P(x=2)=0.22$$, $$P(x=3)=0.28$$, $$P(x=4)=0.20$$, $$P(x=5)=0.14$$, what is the probability that $$x is at $$least 4?

Accepted Answer

$$P(x \geq 4) = 0.20 + 0.14 = 0.34$$

Question 16

Which of the following is a correct step in constructing a discrete probability distribution from frequency data?

Accepted Answer

Divide each frequency by the sum of all frequencies.

Question 17

A distribution has $$P(x=1)=0.5$$, $$P(x=2)=0.3$$, $$P(x=3)=0.2. $$What is the variance $$\$$sigma^2$$ if $$\mu = 1.7$$?

Accepted Answer

$$\$$sigma^2$$ = 0.41$$

Question 18

Which of the following is a real-world example of a continuous random variable?

Accepted Answer

The amount of rainfall in a city during a year.

Question 19

If a probability distribution has a negative probability for one of its outcomes, what does this indicate?

Accepted Answer

The distribution is not a valid probability distribution.

Discrete Probability Distributions: Study Notes for Statistics Students

Study Guide - Practice Questions

Study Guide - Flashcards