AP Statistics Random Variables, Expected Value and Combining Variables Test with Point Values (PDF)
This random variables test for AP Statistics covers random variables, expected value and combining variables (Common Core AP STAT 4.7, AP STAT 4.8, AP STAT 4.9, HSS-MD.A.1, HSS-MD.A.2, HSS-MD.B.5), with a free PDF to print.
Time and points
- Grade: AP Statistics
- Chapter: Random Variables, Expected Value and Combining Variables
- Standards: AP STAT 4.7, AP STAT 4.8, AP STAT 4.9, HSS-MD.A.1, HSS-MD.A.2, HSS-MD.B.5
- Time: 45 minutes
- Total: 20 points
Random variables test: questions
Question 1 – Mean and SD [4 pts]
Let X be the number of siblings. (a) Find the mean. (1 point) (b) Find the standard deviation. (2 points) (c) Interpret the mean. (1 point)
Question 2 – Linear transformation [2 pts]
Profit is Y = 5X – 20 where X has mean 12 and standard deviation 3. Find the mean and standard deviation of Y.
Question 3 – Independent sum [3 pts]
Two independent machines make parts with mean lengths 20 cm and 30 cm and standard deviations 0.3 and 0.4. Find the mean and standard deviation of the total length, and of the difference (longer minus shorter). (3 points)
Question 4 – Fair game [3 pts]
(a) Find the expected net gain. (2 points) (b) Is the game fair? (1 point)
Question 5 – Variances add [2 pts]
X and Y are independent, with standard deviations 6 and 8. Find the standard deviation of X + Y and explain why it is not 14.
Question 6 – 2X versus X + Y [2 pts]
X has mean 5 and standard deviation 2. Y is an independent copy. Find the mean and sd of 2X and of X + Y.
Question 7 – Insurance [2 pts]
A warranty costs $60. It pays $400 with probability 0.1 and nothing otherwise. Find the expected profit to the seller per warranty.
Question 8 – Valid distribution [2 pts]
X takes values 1, 2, 3, 4 with probabilities 0.15, 0.35, k, 0.25. Find k and P(X >= 3).
Key facts behind this random variables test
- Probabilities in a distribution are between 0 and 1 and sum to 1.
- Mean (expected value): sum of x p; interpret it as the long-run average.
- Standard deviation: square root of the sum of (x – mean)^2 p.
- For a + bX: mean a + b mu, standard deviation |b| sigma.
- For independent X, Y: means add or subtract; variances add (also for X – Y).
How to use this random variables test
Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.
All AP Statistics chapters: AP Statistics math.
Free printable PDF
AP Statistics Random Variables, Expected Value and Combining Variables Test with Point Values
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