AP Statistics Chapter 7 Review
Name:________________
Date:_______ Period:____
NOTE: On Monday when you return, there will be a three question quiz based on this review sheet. Answers to the review sheet will be
posted on the website at the end of the week off!
1.
Suppose X is a random variable with mean
 . Suppose we observe X many times and keep tack of the
average of the observed values. What does the law of large numbers say about this situation?
2. In a population of students, the number of pets owned is a random variable X with P(X = 0) = .1, P(X = 1) = .3
and P(X = 2) = .5
(a) If X takes on the values 0, 1, 2, and 3, what is P(X = 3)? _________
(b) Find the mean of X ________
(c) Find the variance of X _______
3. The number of words in an English term paper for a group of students has a normal distribution with mean
2600 and standard deviation 72. What is the probability that the next paper in the stack exceed 2500
words? __________
4. A teacher studied the number of times students laughed out loud during her class. Let X be the number of
laughs in the hour. X had the following distribution:
X
0
1
2
3
4
Probability
0.05
0.2
0.3
0.3
0.15
a) What is the probability that a randomly chosen student laughs at least 3 times during the class? _________
b) What is P(X < 2) ______
c) What is P(X = 1) ______
d) Is this is discrete or continuous random variable? ______________
e) What is the mean of X? __________
f) What is the variance of X? ________
g) What is the standard deviation of X? ___________
h) Define a new random variable Y = 2X – 1…create a probability distribution for Y and check your answers with
the rules.
i) Find the mean of Y? ________
ii) Find the variance of Y? ________
iii) Find the standard deviation of Y? _______
6. Describe the difference between a discrete and continuous random variable.
7. You decide to play a game in which two dice are rolled and the sum of the numbers is recorded. It costs you
$10.00 to play. You win $20.00 if a sum of a 2 or 12 comes up, $10.00 if a sum of a 3 or 11 is rolled, $5.00 if a
sum of a 4, 9 or 10 is rolled. You win nothing for every other sum.
a) Identify the random variable ______________
b) Construct a probability distribution of this variable
c) Find the expected value of this game. ____________
d) Is this game fair? Why or why not? And if not, how much would need to be charged in order to
make the game fair?
8. During the holiday season, you have been scoping out the price of a new 20” flat screen TV. Your research
tells you that the price of this TV is normally distributed with a mean of $179.00 and a standards deviation of
$18.00.
a) What is the probability that the next store you go into has is for less than $150.00? ________
b) The probability is about 70% that the price is below what amount? __________
9. A continuous probability distribution consists of 3 line segments containing the points (0, .2), (1, .3), (3, .3)
and (4, 0).
a) Sketch this probability distribution function and confirm it is a valid one.
b) Find P(0 < X < 2) _________
c) Find P( X
 3 ) _________
d) Find P(X = 2) _________
e) Find P( 3 
X  4 ) ________
10. The number of calories in a candy cane is a random variable with mean 90. The number of calories in a
handful of holiday M&M’s is a random variable with a mean 250. You are splurging one nutrition break and have
both the candy cane and the handful of M&M’s. Let Z be the random variable that represents the total number
of calories in this treat. What is the mean of Z? _________
11. If
 X  62 .  X  4.5 , Y  122 and  Y  10.2 assuming that X and Y are independent.
a) Find  X Y
c) Find  X Y
e) If Z = 3X + 4, Find  Z and  Z
b) Find  X Y
d) Find  X Y