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Unit 4

4.14 MC Answers and Review

6 min read•june 18, 2024

AP Statistics 📊

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Answers and Review for Multiple Choice Practice on Probability, Random Variables, and Probability Distributions

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⛔STOP ⛔ Before you look at the answers make sure you gave this practice quiz a try so you can assess your understanding of the concepts covered in Unit 4. Click here for the practice questions: AP Statistics Unit 4 Multiple Choice Questions.

Facts about the test: The AP Statistics exam has 40 multiple choice questions and you will be given 1 hour 30 minutes to complete the section. That means it should take you around 11 minutes to complete 5 questions.

The following questions were not written by College Board and although they cover information outlined in the AP Statistics Course and Exam Description the formatting on the exam may be different.

1. Which of the following is the set of all possible outcomes of a given event?

A. Frequency Chart

B. Simulation Chart

C. Sample Space

D. Tree Diagram

Answer: A sample space is any way in which all possible outcomes of a given event are listed out.

📄 Study AP Statistics, Unit 4.3: Introduction to Probability

2. Which of the following two events represents two events that are mutually exclusive?

A. December in FL and hurricane

B. January in CA and snow

C. November in NY and rain

D. July in AL and snow

Answer: July in AL and snow is an example of mutually exclusive events because they cannot occur at the same time. All of the other examples could occur and likely do at the same time.

📄 Study AP Statistics, Unit 4.4: Mutually Exclusive Events

3. If there are 6 items in a hat: 4 marbles (2 red and 2 blue) and 2 coins (1 red and 1 blue). What is the probability of drawing a marble or blue?

A. 5/6

B. 4/6

C. 1/6

D. 3/6

Answer: Since this is an or probability, otherwise known as a union of events, we take the 4 marbles and the 1 blue coin and add those up as our successes, which gives us 5/6. The red coin is the only option that doesn't fit our description.

📄 Study AP Statistics, Unit 4.3: Introduction to Probability

4. Which of the following events are independent of each other?

A. Month of year and rain

B. Day of week and rain

C. Month of year and snow

D. Temperature and snow

Answer: Since day of the week and snow chances don't affect each other, they are independent of each other.

📄 Study AP Statistics, Unit 4.6: Independent Events and Unions of Events

5. Which of the following is not one of the classifications for a binomial distribution?

A. Independence

B. Clear success and failure

C. Normal Distribution

D. All trials equally likely of success

Answer: The binomial distribution is its own type of distribution, therefore, it does not follow a normal distribution always (it is usually skewed right instead of symmetric)

📄 Study AP Statistics, Unit 4.11: Parameters for a Binomial Distribution

6. If a given random variable X has a mean of 3.2, what would the mean of random variable Y be if Y=X+5?

A. 3.5

B. 5.2

C. 3.2

D. 8.2

Answer: When transforming a random variable by addition, the mean changes based on that change. Scalar addition changes the mean, but not the standard deviation.

📄 Study AP Statistics, Unit 4.8: Mean and Standard Deviation of Random Variables

7. If a given random variable X has a standard of 0.7, what would the mean of random variable Y be if Y=5X?

A. 0.7

B. 3.5

C. 1.2

D. 5

Answer: When transforming a random variable by multiplication, the mean and standard deviation both are multiplied by the scalar.

📄 Study AP Statistics, Unit 4.8: Mean and Standard Deviation of Random Variables

8. A random variable is decided to follow a geometric distribution with a p=0.4. Find the mean of the geometric variable.

A. 0.4

B. 40

C. 4

D. 2.5

Answer: The formula for the mean of a geometric distribution is 1/p, so 1/0.4 is 2.5.

📄 Study AP Statistics, Unit 4.12: The Geometric Distribution

9. Joseph is going to flip a coin until he gets a heads. What type of distribution would this describe?

A. Geometric

B. Binomial

C. Normal

D. Uniform

Answer: Since Joseph is repeating the trial until he gets a success, this is a geometric distribution.

📄 Study AP Statistics, Unit 4.12: The Geometric Distribution

10. You are playing a game where you roll the dice, you win $5 if you get a 1 or a 6, $2 if you roll a 3 or -$2 if you roll a 2 or a 4. What is the expected value?

A. $10

B. $2

C. $1.33

D. $0

Answer: The expected value can be found by taking the sum of all possible outcomes multiplied by their individual probabilities: (2/6*5)+(1/6*2)+(2/6*-2).

📄 Study AP Statistics, Unit 4.9: Combining Random Variables

11. Which of the following statements is always false?

A. P(A)=P(B) if A and B are independent

B. P(A)>P(B) if P(A) is independent.

C. P(A)=1.5

D. P(A)=0.5 and P(B)=0.5, then A and B are mutually exclusive

Answer: Since any and all probabilities are between 0 and 1, it is impossible for P(A) to be 1.5.

📄 Study AP Statistics, Unit 4.3: Introduction to Probability

12. If there are 6 red marbles and 12 blue marbles in a jar, what is the probability of drawing 3 red marbles (without replacement) from the jar in a row?

A. 0.043

B. 0.5

C. 0.33

D. 0.43

Answer: Since we are drawing three marbles without replacement, we would find the probability at each trial of selecting a red marble: 6/18 for the first trial, 5/17 for the second, 4/16 for the third and then multiply our three probabilities since these events are independent of each other.

📄 Study AP Statistics, Unit 4.0: Unit 4 Overview

13. Let X be the outcome of a regular dice. Find P(2<X<5).

A. 1

B. 0.5

C. 0.66

D. 0.33

Answer: Since the only options that are less than 5 and greater than 2 are 3 and 4, these are the two outcomes out of the 6 possible outcomes that satisfy our bounds. Therefore, 2/6=0.33

📄 Study AP Statistics, Unit 4.0: Unit 4 Overview

14. Which of the following are not associated with the normal distribution density curve?

A. Symmetric

B. Bell Shaped

C. Unimodal

D. Uniform

Answer: The normal distribution is not uniform, meaning that every outcome is not equally likely. It is a curve, not a rectangle.

📄 Study AP Statistics, Unit 4.1: Introducing Statistics: Random and Non-Random Patterns?

15. What data set would be an example of a continuous random variable?

A. Day of the week on which you were born

B. Shoe Size

C. Height

D. Grade in school

Answer: Since shoe size, day of the week for birthday and grade in school are all either whole numbers or categorical variables, they are discrete. Height is much more flexible (you could be 62.768 inches tall), so it is a continuous random variable.

📄 Study AP Statistics, Unit 4.7: Introduction to Random Variables and Probability Distributions

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