Question 1

Which of the following best describes a discrete random variable?

Accepted Answer

A variable whose values are determined by chance and can only take on countable values.

Question 2

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

Accepted Answer

Each outcome must have the same probability.

Question 3

Suppose you toss two coins. What is the probability of getting exactly one head?

Accepted Answer

$$\frac{1}{2}$$

Question 4

Given a discrete probability distribution with mean $$\mu = 1.0$$ and standard deviation $$\sigma = 0.7$$, what is the range of values that are NOT considered significant according to the range rule of thumb?

Accepted Answer

Between $$-0.4$$ and $$2.4$$

Question 5

Which formula correctly represents the mean (expected value) of a discrete probability distribution?

Accepted Answer

$$\mu = \sum x \cdot P(x)$$

Question 6

A binomial experiment must satisfy all of the following EXCEPT:

Accepted Answer

The probability of success changes from trial to trial.

Question 7

If $$p = 0.3 is $$the probability of success in a binomial experiment, what is the probability of failure $$q$$?

Accepted Answer

$$q = 0.7$$

Question 8

Which formula gives the probability of exactly $$x$$ successes in $$n$$ binomial trials?

Accepted Answer

$$P(x) = \frac{n!}{x!(n-x)!} p^x q$$^{n-x}$$

Question 9

A survey finds that 40% of males between age 30 and 40 smoke. If 15 males are selected at random, what is the expected number of smokers?

Accepted Answer

$$6$$

Question 10

In a binomial distribution with $$n = 12$$ and $$p = 0.95$$, what is the variance?

Accepted Answer

$$0.57$$

Question 11

A random variable $$X$$ has the following probability distribution: $$P(0) = 0.25$$, $$P(1) = 0.5$$, $$P(2) = 0.25. $$What is the expected value $$E(X)$$?

Accepted Answer

$$1.0$$

Question 12

If a random sample of 8000 births is taken and 2% result in twins, what is the standard deviation for the number of twin births?

Accepted Answer

$$12.6$$

Question 13

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

Accepted Answer

Counting the number of defective items in a batch of 20, where each item is either defective or not.

Question 14

A company finds 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?

Accepted Answer

$$0.163$$

Question 15

If the mean number of successful sales per week is 4 and the standard deviation is 1.2, what is the range of values that are NOT considered significant according to the range rule of thumb?

Accepted Answer

Between $$1.6$$ and $$6.4$$

Question 16

Which of the following is a continuous random variable?

Accepted Answer

The body temperature of a randomly selected person.

Question 17

If $$n = 10$$, $$p = 0.2$$, and $$q = 0.8$$, what is the mean of the binomial distribution?

Accepted Answer

$$2$$

Question 18

Which of the following statements about probability distributions is TRUE?

Accepted Answer

The sum of all probabilities in a probability distribution must equal 1.

Discrete and Binomial Probability Distributions: Concepts, Formulas, and Applications

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