Unit 4: Probability & Random Variables
Statistics · Unit 4 · Paper 2

Probability & Random Variables unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1Paper 2Paper 3
Each paper is built from this unit’s 20 terms and is the same for everyone, so a teacher can assign “Unit 4, Paper 2” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.
Suggested time 36 min 33 points0/17 attempted
1

Binomial setting

2

Simulation design

3

Conditional probability

4

"At least one" problems

5

Binomial mean and standard deviation

6

Independence of two random variables

7

Binomial vs geometric on the exam

8

Linear transformation of a random variable

9

Variance of a random variable

10

Geometric setting

11

Two-way table probabilities

12

Addition rule

Short answer 1. Define or explain: Law of large numbers

3 pts

Short answer 2. Define or explain: Tree diagrams

3 pts

Short answer 3. Define or explain: 10% condition

3 pts

Short answer 4. Define or explain: Mutually exclusive vs independent

3 pts

Free response

9 pts

This course has no free-response prompt tagged to this unit, so one from elsewhere in the course is used. It is still worth writing — the skill transfers.

A coffee chain claims that 60% of its customers prefer its new house blend. A skeptical manager suspects the true proportion is lower. In a random sample of 150 customers, 78 prefer the new blend. Use α = 0.05.

State the hypotheses, defining the parameter in context.

Verify the conditions for a one-proportion z-test.

Calculate the test statistic and the P-value.

State a conclusion in the context of the problem.

Describe a Type I error in this context and its consequence for the chain.