Question 1

Which of the following is a requirement for a probability distribution?

Accepted Answer

Each probability must be between 0 and 1, inclusive.

Question 2

A random variable $$X$$ represents the number of heads in three tosses of a fair coin. What is the probability that $$X = 2$$?

Accepted Answer

$$\frac{3}{8}$$

Question 3

Which of the following best describes a discrete random variable?

Accepted Answer

It has a countable number of possible values.

Question 4

Given the following probability distribution for the number of items bought at a store: $$P(1) = 0.32$$, $$P(2) = 0.12$$, $$P(3) = 0.23$$, $$P(4) = 0.18$$, $$P(5) = 0.15. $$What is the expected number of items bought?

Accepted Answer

$$2.98$$

Question 5

Which of the following is NOT a requirement for a binomial experiment?

Accepted Answer

The probability of success changes from trial to trial.

Question 6

A die is rolled three times. What is the probability of getting exactly two sixes?

Accepted Answer

$$\frac{15}{216}$$

Question 7

If $$X is a $$binomial random variable with $$n = 10$$ and $$p = 0.3$$, what is the mean $$\mu of$$ $$X$$?

Accepted Answer

$$3$$

Question 8

A survey found that 30% of teenagers have part-time jobs. If 5 teenagers are selected at random, what is the probability that at least 3 have part-time jobs? (Use the binomial formula.)

Accepted Answer

$$0.163$$

Question 9

Which formula gives the variance $$\$$sigma^2$$ of a binomial distribution with parameters n$ and p$?

Accepted Answer

$$\$$sigma^2$$ = np(1-p)$$

Question 10

In a World Series that can last between 4 and 7 games, the number of games played is a:

Accepted Answer

Discrete random variable

Question 11

If the probability of an event is 0.2, what is the probability that the event does NOT occur?

Accepted Answer

$$0.8$$

Question 12

A binomial experiment has $$n = 8$$ and $$p = 0.25. $$What is the standard deviation $$\sigma$$?

Accepted Answer

$$1.22$$

Question 13

Which of the following scenarios is best modeled by a binomial distribution?

Accepted Answer

Counting the number of heads in 10 coin tosses.

Question 14

If $$X is a $$discrete random variable with the following probability distribution: $$P(0) = 0.1$$, $$P(1) = 0.3$$, $$P(2) = 0.4$$, $$P(3) = 0.2$$, what is $$E[X]$$?

Accepted Answer

$$1.7$$

Question 15

A casino game pays $$10 with probability 0.1 and loses 2 $$with probability 0.9. What is the expected value of a single play?

Accepted Answer

$$-0.80$$

Question 16

In a binomial experiment, which Excel function can be used to find the probability of exactly $$k$$ successes in $$n$$ trials with probability $$p of $$success?

Accepted Answer

=BINOM.DIST(k, n, p, 0)

Question 17

If the mean $$\mu of a $$binomial distribution is 20 and the standard deviation $$\sigma is 3$$, what is the range of values considered 'not significant' according to the range rule of thumb?

Accepted Answer

Between $$14$$ and $$26$$

Question 18

A survey found that 58% of American adults use the Internet. If 20 adults are selected at random, what is the expected number who use the Internet?

Accepted Answer

$$11.6$$

Question 19

Which of the following is a parameter of a probability distribution?

Accepted Answer

Population mean

Question 20

In a binomial experiment with $$n = 5$$ and $$p = 0.4$$, what is the probability of getting exactly 3 successes? (Use the binomial formula.)

Accepted Answer

$$0.2304$$

Probability Distributions and the Binomial Distribution

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