Unit 2: Probability, Random Variables, and Probability Distributions
Statistics · Unit 2 · Paper 1

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 1Paper 2Paper 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 1” 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
1

Unbiased does not mean correct

2

General multiplication rule

3

Effect of n on shape

4

Addition rule

5

Binomial mean and standard deviation

6

Large counts condition

7

Marginal versus joint probability

8

Why standard error shrinks with n

9

Binomial probability formula

10

Shape of the sampling distribution of p̂

11

Effect of n on center

12

Law of large numbers

Short answer 1. Define or explain: Geometric setting

3 pts

Short answer 2. Define or explain: Requirements of a probability distribution

3 pts

Short answer 3. Define or explain: Sample space

3 pts

Short answer 4. Define or explain: Spread of the sampling distribution of p̂

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.