Question 1

Which of the following best describes a conditional distribution in the context of a contingency table?

Accepted Answer

It is the relative frequency of each category of the response variable, given a specific value of the explanatory variable.

Question 2

A medical study finds that 30% of patients with a certain disease are smokers, while only 10% of patients without the disease are smokers. What statistical concept does this scenario best illustrate?

Accepted Answer

Conditional distribution

Question 3

Which formula correctly represents the probability of the union of two events $$A$$ and $$B$$?

Accepted Answer

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

Question 4

A fair die is rolled twice. What is the probability of getting a 6 on at least one roll?

Accepted Answer

$$\frac{11}{36}$$

Question 5

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

Accepted Answer

The probability of success changes from trial to trial.

Question 6

If $$X is a $$binomial random variable with $$n=10$$ and $$p=0.3$$, what is the expected value $$E[X]$$?

Accepted Answer

$$E[X] = 3$$

Question 7

Which of the following statements about independent events is TRUE?

Accepted Answer

If $$A$$ and $$B$$ are independent, then $$P(A \cap B) = P(A) 	imes P(B).$$

Question 8

A probability model assigns probabilities to each outcome in a sample space such that:

Accepted Answer

The sum of the probabilities is exactly 1.

Question 9

Suppose a random variable $$X$$ has the following probability distribution: $$P(X=0)=0.2$$, $$P(X=1)=0.5$$, $$P(X=2)=0.3. $$What is the mean of $$X$$?

Accepted Answer

$$1.3$$

Question 10

Which of the following best describes the Law of Large Numbers?

Accepted Answer

As the number of trials increases, the sample mean approaches the population mean.

Question 11

A normal distribution is completely described by which two parameters?

Accepted Answer

Mean and standard deviation

Question 12

If a normal random variable $$X$$ has mean $$\mu = 50$$ and standard deviation $$\sigma = 10$$, what is the $$z-$$score for $$X = 70$$?

Accepted Answer

$$z = 2$$

Question 13

Which of the following is a property of the normal density curve?

Accepted Answer

It is symmetric about the mean.

Question 14

A researcher wants to find the probability that a randomly selected value from a normal distribution is less than a certain value $$x. $$Which of the following should they use?

Accepted Answer

The area under the normal curve to the left of $$x$$

Question 15

Which of the following is the correct formula for the mean of a discrete random variable $$X$$ with possible values $$x_i$$ and probabilities $$p_i$$?

Accepted Answer

$$\sum x_i p_i$$

Question 16

A binomial experiment consists of 5 trials with probability of success $$p=0.4. $$What is the probability of exactly 2 successes? (Use the binomial formula.)

Accepted Answer

$$0.2304$$

Question 17

Which of the following is NOT a characteristic of a probability distribution for a discrete random variable?

Accepted Answer

The random variable can take on any value in an interval.

Question 18

If two events $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cap B)$$?

Accepted Answer

$$0$$

Question 19

A sample of 100 batteries is tested, and the sample mean lifetime is found to be 500 hours. If the population mean is 495 hours, what is the sampling error?

Accepted Answer

$$5$$ hours

Question 20

Which of the following best describes a simple random sample?

Accepted Answer

A sample in which every possible sample of the same size has an equal chance of being selected.

Introductory Statistics Study Guide: Probability, Distributions, and Sampling

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