Probability and Statistics Quizzes: Test Your Knowledge

Question 1

Which of the following is the probability of rolling a number greater than 2 on a standard six-sided die?

Accepted Answer

1/2

Answer

1/3

Answer

2/5

Answer

1/4

Question 2

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is drawn at random, what is the probability that it is not green?

Accepted Answer

7/10

Answer

9/10

Answer

3/10

Answer

1/5

Question 3

A random variable X represents the number of times a team wins in a sequence of games. If the probability of winning a single game is 0.6, what is the probability that the team wins exactly 3 games out of 5?

Accepted Answer

0.32768

Answer

0.4096

Answer

0.20736

Answer

0.10368

Question 4

The mean of a normal distribution is 50 and the standard deviation is 10. What is the probability that a randomly selected value from this distribution is less than 40?

Accepted Answer

0.02275

Answer

0.00621

Answer

0.01972

Answer

0.15866

Question 5

Which of the following measures the central tendency of a distribution?

Accepted Answer

Mean

Answer

Standard deviation

Answer

Range

Answer

Variance

Question 6

A dataset has a range of 20 and a variance of 25. What is the standard deviation of the dataset?

Accepted Answer

5

Answer

12

Answer

10

Answer

2

Question 7

Which of the following is a measure of the spread or variability of a distribution?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Mode

Answer

Median

Question 8

A sample of data has a skewed distribution. Which of the following measures of central tendency is most appropriate?

Accepted Answer

Median

Answer

Mode

Answer

Range

Answer

Mean

Question 9

Which of the following statistical techniques is used to make predictions about a population based on a sample?

Accepted Answer

Hypothesis testing

Answer

Factor analysis

Answer

Correlation analysis

Answer

Regression analysis

Question 10

Which of the following is NOT a fundamental concept of probability?

Accepted Answer

Mean

Answer

Event

Answer

Random variable

Answer

Statistical distribution

Question 11

A random variable is a function that assigns a numerical value to each outcome of an experiment. What is the range of a random variable?

Accepted Answer

The set of all possible outcomes

Answer

The set of all integers

Answer

The set of all positive numbers

Answer

The set of all real numbers

Question 12

Which of the following is a type of discrete statistical distribution?

Accepted Answer

Binomial

Answer

Normal

Answer

Poisson

Answer

Exponential

Question 13

The probability density function (PDF) of a continuous random variable is:

Accepted Answer

Non-negative

Answer

Always equal to 1

Answer

Positive

Answer

Negative

Question 14

Which of the following is NOT a property of the expected value (mean) of a random variable?

Accepted Answer

It is always positive

Answer

It represents the long-run average value

Answer

It can be used to compare different random variables

Answer

It is a weighted average of all possible outcomes

Question 15

In a fair coin toss experiment, what is the probability of getting heads or tails?

Accepted Answer

0.5

Answer

1.0

Answer

0.75

Answer

0.25

Question 16

Which of the following is NOT a type of sampling method?

Accepted Answer

Biased sampling

Answer

Cluster sampling

Answer

Stratified sampling

Answer

Simple random sampling

Question 17

What is the purpose of a confidence interval?

Accepted Answer

To estimate a parameter of a population

Answer

To test a hypothesis

Answer

To determine the probability of an event

Answer

To predict future events

Question 18

Which of the following is a key assumption of the Central Limit Theorem?

Accepted Answer

Sample size is large enough

Answer

Data is normally distributed

Answer

Sample is unbiased

Answer

Population mean is known

Question 19

What is the difference between a statistic and a parameter?

Accepted Answer

A statistic is a characteristic of a sample, while a parameter is a characteristic of a population

Answer

A parameter is always known, while a statistic is not

Answer

A statistic is always a number, while a parameter is not