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CCHS
AP Statistics
Chapter 7.1-7.5
Review
Name __________________________ Date________ Period_____
Determine if the following are examples of discrete or continuous variables and explain your
reasoning.
1. The number of books in your book bag.
4. The height of the basketball team members.
2. The weight of your book bag.
5. The time it takes to finish a math exam.
3. The number of days it snows in a year.
6. The number of cars that go through a tunnel in
an hour.
Make a discrete probability distribution using the following data.
7. The number of books in a book bag are as follows for a class of 20 students.
1
2
4
3
1
1
3
3
5
4
2
3
2
2
3
5
2
2
4
3
X
P(x)
Remember: The mean (expected value) of a probability distribution is ∑ x ∗ p (x)
8. The number of children per family in a certain community is given in the following table:
X, number of children 1
2
3
4
P(x)
0.3 0.4 0.2 0.1
Find the mean number of children for this community.
Find the expected value for the following examples.
9. The local fire department plans to sell 500 raffle tickets for $2 each. First prize is $100, Second prize is
$50, and Third prize is $25.
Gain, x
Probability, P(x)
What is the expected value?
How much money would the fire department have left after paying out the prizes with this fund raiser?
Mambou
12/12/2014
CCHS
10. A carnival worker is tempting you to play his game. He has a secret box which contains twenty $1 bills,
ten $5 bills, and five $10 bills. You can draw one bill out per game; however, the cost of the game is $5.
Fill in the table for the profit you might win.
Gain, x
Probability, P(x)
What is the expected value of the game?
Should you play?
Determine if the each of the following is a probability distribution or not. Explain your reasoning.
11.
0
1
2
3
4
x
0.1
0.2
0.1
0.5
0.2
P(x)
12.
x
P(x)
1
¼
2
0
3
½
4
¼
Construct a probability distribution for the following data.
13. Number of televisions in a sample of households.
X, # of tv’s
Households
P(X)
0
87
1
223
2
315
14. Number of times students were tardy to class the first quarter.
X, # of tardies
0
1
2
# of students
80
20
22
P(X)
3
193
4
97
3
18
4
10
15. Make a probability distribution for the number of heads when a fair coin is tossed 3 times.
(Hint: Drawing a sample space will help).
X, # of heads
P(X)
What is the average number of heads you can expect?
16. Make a probability distribution for the number of boys in a family with two children.
(Hint: Drawing a sample space will help).
X, # of boys
P(X)
What is the average number of boys in a family with two children?
Mambou
12/12/2014
CCHS
7.5 Review
1. Which of the following are binomial distributions? Explain each answer.
a. Asking 100 students if they ate lunch today.
b. Asking the students in your class how they got to school today.
c. Drawing a club from a deck of cards.
d. Rolling a die to see the outcome.
e. Eating 3 different brands of hamburgers to find the favorite one.
f. Tossing a coin until you get a head.
g. Surveying 1000 students to see if they have a dog.
For each binomial distribution, find the probability. First, write your numbers in the formula, then use
either the calculator or the table.
P(r )= n C r ∗ p r ∗ q ( n − r ) Remember that. q = 1 − p
2. Ryan is taking a twenty question true-false exam and plans to guess on each problem. Find the
probability that he will get exactly 16 of the twenty questions correct.
3.
Stephen is taking a twenty question multiple choice test. Each question has 5 choices, A,B,C,D or E.
Only one of the five is correct.
If Stephen guesses on every problem, what is the probability that he will get exactly 8 correct?
Mambou
12/12/2014
CCHS
4. Suppose that 30% of the vehicles in a mall parking lot belong to employees. Nine vehicles are
chosen at random. Find the probability that:
a. Exactly 3 belong to mall employees.
b. At most 3 belong to mall employees.
c. At least 7 belong to mall employees.
5. If 3 out of 4 nursing majors are female, find the probability that 2 out of 7 will be female.
6. A survey indicates that 23% of US men select fishing as their favorite leisure activity.
a. Is this a binomial distribution? _________________________
b. Is it possible to use the table for this problem? Explain. _____________________
c. If you randomly select 5 men, find the probability that exactly two of the men liked fishing.
d. Again, if you randomly select 5 men, find the probability that at least 2 of the men liked
fishing.
Mambou
12/12/2014
CCHS
Chapter 5 Section 5.1 Practice Name _KEYS_____ Date_December 12, 2014_ Period__2B/1A__
Determine if the following are examples of discrete or continuous variables and explain your reasoning.
1. The number of books in your book bag.
Discrete
2. The weight of your book bag.
Continuous
3. The number of days it snows in a year.
Discrete
4. The height of the basketball team members.
Continuous
5. The time it takes to finish a math exam.
Continuous
6. The number of cars that go through a tunnel in an hour.
Discrete
Make a discrete probability distribution using the following data.
7. The number of books in a book bag are as follows for a class of 20 students.
1
2
4
3
X
P(x)
1
1
3
3
1
5
4
2
3
20
6
20
2
3
2
2
3
5
2
2
4
3
3
4
5
6
20
3
20
2
20
Remember: The mean (expected value) of a probability distribution is
∑ x ∗ p (x)
8. The number of children per family in a certain community is given in the following table:
X, number of children
1
2
3
4
P(x)
0.3 0.4 0.2 0.1
Find the mean number of children for this community.
∑ x ∗ p (x) = 0.3*1+2*0.4+3*0.2+4*0.1= 2.1
Find the expected value for the following examples.
9. The local fire department plans to sell 500 raffle tickets for $2 each. First prize is $100, Second prize is $50, and Third prize is
$25.
-2
23
48
98
Gain, x
Probability, P(x)
497
1
1
1
500
500
500
500
What is the expected value? ∑ x ∗ p (x) = -$1.65
How much money would the fire department have left after paying out the prizes with this fund raiser?
$825
10. A carnival worker is tempting you to play his game. He has a secret box which contains twenty $1 bills, ten $5 bills, and five
$10 bills. You can draw one bill out per game; however, the cost of the game is $5. Fill in the table for the profit you might win.
-4
0
5
Gain, x
Probability, P(x)
20
5
10
What is the expected value of the game?
35
35
35
∑ x ∗ p (x) = -$1.57. Should you play? No should not play, because the
expected value is negative that means in each ticket you loose $ 1.57.
Determine if the each of the following is a probability distribution or not. Explain your reasoning.
11.
0
1
2
3
4
x
0.1
0.2
0.1
0.5
0.2
P(x)
Not a probability distribution because ∑ x ∗ p (x) = 1.1
12.
x
P(x)
Mambou
1
¼
2
0
3
½
4
¼
12/12/2014
CCHS
Yes it is because ∑ x ∗ p (x) = 1. And each probability is between 0 and one included.
Construct a probability distribution for the following data.
13. Number of televisions in a sample of households.
X, # of tv’s
Households
P(X)
0
87
1
223
2
315
3
193
4
97
87
915
223
915
315
915
193
915
97
915
2
22
3
18
4
10
22
150
18
150
10
150
14. Number of times students were tardy to class the first quarter.
X, # of tardies
0
1
# of students
80
20
P(X)
20
80
150
150
15. Make a probability distribution for the number of heads when a fair coin is tossed 3 times.
(Hint: Drawing a sample space will help).
X, # of heads
0
1
2
P(X)
1
4
2
8
8
What is the average number of heads you can expect?
8
∑ x ∗ p (x) = 1.375
16. Make a probability distribution for the number of boys in a family with two children.
(Hint: Drawing a sample space will help).
X, # of boys
0
1
P(X)
1
2
4
What is the average number of boys in a family with two children?
Mambou
3
1
8
4
2
1
4
∑ x ∗ p (x) = 1
12/12/2014