AnswersCommon Core Algebra II - MA3111 B-ICBinomial Distribution

Binomial Distribution Answers

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Mrs. Gomes found that 40% of students at her high school take chemistry. She randomly surveys 12 students. What is the probability that exactly 4 students have taken chemistry? Round the answer to the nearest thousandth.

Question illustration
A
0.005
B
0.008
C
0.213
D
0.227
2
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Forty-four percent of the members of the Science Club wear blue shirts. Which of the following is a binomial experiment?

A
Selecting eight members randomly and recording whether each member is wearing a blue shirt
B
Selecting eight members randomly and recording the number in the group wearing a blue shirt
C
Selecting members randomly until one without a blue shirt is chosen
D
Selecting members randomly until one with a blue shirt is chosen
3

According to a poll, 30% of voters support a ballot initiative. Hans randomly surveys 5 voters. What is the probability that exactly 2 voters will be in favor of the ballot initiative? Round the answer to the nearest thousandth.

Question illustration
A
0.024
B
0.031
C
0.132
D
0.309
4

Which of the following is a binomial experiment?

A
Flipping a coin until it comes up tails
B
Flipping a coin until 8 heads are recorded
C
Flipping a coin 10 times and recording if it comes up heads
D
Flipping a coin by 10 different people and recording the age of each person
5

Two percent of mobile phones produced at a factory are defective. Which of the following is a binomial experiment?

A
Selecting phones randomly until a non-defective phone is chosen
B
Selecting phones randomly until 200 defective phones are chosen
C
Selecting 200 phones randomly and recording whether each phone is defective
D
Selecting a group of phones randomly and recording the number of defective phones in the group
6

Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads?

Question illustration
A
Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed (0.5) Superscript 6
Option A
B
Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed
Option B
C
Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed (0.5) Superscript 9
Option C
D
Subscript 9 Baseline C Subscript 6 Baseline (0.5) Superscript 6
Option D
7

A researcher finds that 15% of all commuters in a metropolitan area take the train to work. The researcher polls 250 people in the area and asks them whether they take the train to work. What is the number of trials for this binomial experiment?

A
15
B
38
C
250
D
265
8

Which of the following is a binomial experiment?

A
A survey asking 75 people to name their favorite color
B
A survey asking 75 people to give their age
C
A survey asking 75 people whom they voted for in the election
D
A survey asking 75 people if they like the new school building
9

Thirty-three percent of all students at a high school like beef stew. Out of 300 students, 40 are selected randomly and asked whether they liked beef stew. If liking beef stew is a success, what is the probability of a failure for this binomial experiment?

A
0.33
B
0.40
C
0.57
D
0.67
10

Janie flips a coin 70 times and records if it comes up heads. If getting heads is a success, what is the probability of a failure?

A
0.2
B
0.5
C
0.7
D
1.00
11

Dion flips a coin 20 times and records if it comes up heads. If getting heads is a success, what is the probability of a success on each flip?

A
0.2
B
0.3
C
0.5
D
1.00
12

Thuy rolls a number cube 7 times. Which expression represents the probability of rolling a 4 exactly 2 times?

Question illustration
A
Subscript 7 Baseline C Subscript 5 Baseline (one-sixth) squared (one-sixth) Superscript 5
Option A
B
Subscript 7 Baseline C Subscript 5 Baseline (one-sixth) Superscript 5 Baseline (five-sixths) squared
Option B
C
Subscript 7 Baseline C Subscript 2 Baseline (one-sixth) squared (five-eighths) Superscript 5
Option C
D
Subscript 7 Baseline C Subscript 2 Baseline (two-sixths) squared (four-sixths) Superscript 5
Option D
13

Franco has a hat with 9 blue marbles, 4 yellow marbles, and 12 green marbles. He designs a binomial experiment by drawing a marble from the hat, recording whether the marble is green, and then laying the marble aside. He then repeats the process seven times. Which statement must be true?

A
The experiment is not a binomial experiment because there is not a fixed number of drawings.
B
The experiment is not a binomial experiment because the probability of choosing a green marble is the same for each drawing.
C
The experiment is not a binomial experiment because the probability of choosing a green marble is not the same for each drawing.
D
The experiment is not a binomial experiment because there are only two possible outcomes for each drawing.
14

How many outcomes are possible for one event of a binomial experiment?

A
1
B
2
C
3
D
4

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