Probability, Random Variables, and Probability Distributions 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 70 terms and is the same for everyone, so a teacher can assign “Unit 2, 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 31 min 28 points0/17 attempted

Tree diagrams

Sampling distribution of x̄

Simulation design

Bias vs variability

Solving at-least-one problems by complement

Standard error

Expected value is not the most likely value

Geometric setting versus binomial

Spread of the sampling distribution of p̂

Why sample size matters more than population size

Binomial mean and standard deviation

Distinguishing three distributions

Short answer 1. Define or explain: 10% condition

3 pts

Short answer 2. Define or explain: Expected value

3 pts

Short answer 3. Define or explain: Independence of two random variables

3 pts

Short answer 4. Define or explain: Law of large numbers

3 pts

Free response

4 pts

At a coffee shop, let X represent the number of drinks purchased by a randomly selected customer. The probability distribution of X is: x 1 2 3 4 P(x) 0.45 0.30 0.18 0.07

A. Calculate and interpret the mean of X.

B. Calculate the standard deviation of X.

C. Two customers are selected at random and independently. Calculate the probability that they purchase a total of exactly 3 drinks.

D. Let T be the total number of drinks purchased by two randomly and independently selected customers. Calculate the mean and standard deviation of T.