Question 1

Which of the following statements about random variables is TRUE?

Accepted Answer

Continuous random variables are measured data, and discrete random variables are counted data.

Question 2

Which of the following best describes the expected value (mean) of a probability distribution?

Accepted Answer

It represents the theoretical average and can be negative.

Question 3

What does the standard deviation of a random variable in a probability distribution describe?

Accepted Answer

How the outcomes vary.

Question 4

Given the variance formula for a discrete probability distribution: $$\$$sigma^2$$ = \sum (x-\mu)^2$ P(x)$$, what is the standard deviation if $$\$$sigma^2$$ = 3.2194$$?

Accepted Answer

$$\sigma = 1.7943$$

Question 5

Which of the following is NOT a condition for using a binomial probability distribution?

Accepted Answer

The probability of success changes from trial to trial.

Question 6

A binomial experiment consists of 8 games of roulette, each with a probability of winning $$p = 0.4734. $$Which of the following statements is TRUE?

Accepted Answer

A binomial probability distribution can be used because there is a fixed number of independent trials, each measuring success or failure.

Question 7

If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$P(A \cap B) = 0.15$$

Question 8

Suppose the odds of event $$E$$ are $$7:2. $$What is the probability $$P(E)$$?

Accepted Answer

$$P(E) = \frac{7}{9}$$

Question 9

A shipment of 5000 batteries has a 5% defect rate. What is the expected number of defective batteries in the shipment?

Accepted Answer

250

Question 10

If $$A$$ and $$B$$ are not mutually exclusive events, which formula gives $$P(A \cup B)$$?

Accepted Answer

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Question 11

In a standard deck of 52 cards, what is the probability of drawing a card that is either a face card or a heart?

Accepted Answer

$$P = \frac{22}{52}$$

Question 12

Which of the following is a property of a discrete probability distribution?

Accepted Answer

The sum of all probabilities is 1.

Question 13

If $$P(E) = 0.3$$, what is $$P(E^c)$$, the probability of the complement of $$E$$?

Accepted Answer

$$P(E^c) = 0.7$$

Question 14

A random variable $$X$$ has the following probability distribution: $$P(1) = 0.15$$, $$P(2) = 0.275$$, $$P(3) = 0.1125$$, $$P(4) = 0.15$$, $$P(5) = 0.0875$$, $$P(6) = 0.225. $$What is $$\mu = E[X]$$?

Accepted Answer

$$\mu = 3.425$$

Question 15

In a binomial experiment with $$n = 10$$ and $$p = 0.52$$, what does the random variable $$X$$ represent?

Accepted Answer

The number of successes in 10 trials.

Introductory Statistics Practice Exam Guidance: Probability, Random Variables, and Binomial Distributions

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