Statistics · Unit 4 · Paper 3

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 1 Paper 2 Paper 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 3” 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

Addition rule

Binomial mean and standard deviation

"At least one" problems

Mutually exclusive vs independent

Expected value

Independence of two random variables

Binomial vs geometric on the exam

Simulation design

Conditional probability

Checking independence

Complement rule

Two-way table probabilities

Short answer 1. Define or explain: Variance of a random variable

3 pts

Short answer 2. Define or explain: Combining random variables

3 pts

Short answer 3. Define or explain: Law of large numbers

3 pts

Short answer 4. Define or explain: Binomial setting

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 machine fills bags of trail mix. The weights of the bags are approximately normally distributed with mean 452 grams and standard deviation 8 grams.

Find the probability that a randomly selected bag weighs less than 440 grams, and interpret it in context.

A quality inspector takes a random sample of 16 bags. Describe the sampling distribution of the sample mean weight x̄ (shape, center, and spread), justifying each feature.

Find the probability that the mean weight of the 16 sampled bags is less than 448 grams.

The inspector actually observes x̄ = 448 grams. Using your answer to part (c), explain whether this provides convincing evidence that the machine is now underfilling (that is, that the true mean has dropped below 452 grams).