Statistics & Probability
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7th Grade Math › Statistics & Probability
After a school choir concert, the music teacher wanted to know what the student body thought about the song choices. Select the option that best represents a sample.
Everyone who was at the choir concert
All of the teachers
The girls that attend the school
A random selection of the students who were at the concert
Explanation
In order to answer this question we first need to know what "sample" means. A sample is a subset of a population.
Because we want a subset, we don't want the entire population, which eliminates the answer choice "Everyone who was at the choir concert ". Also, the teacher wants to know what the student body thought about the songs, not the teachers, which eliminates "All of the teachers". Finally, the music teacher didn't specify if she wanted just the girls' opinions, which makes "A random sample of the students who were at the concert" the best answer choice.
A bag contains red marbles,
pink marbles, and
purple marbles. What is the probability of not choosing a purple marble?
Explanation
The probability (p) is equal to the number of a specific event (purple marbles) divided by the total number of events. The probability of NOT p (called q) is equal to In this example:
In a dice game, what is the probability of rolling a factor of 5 on a six-sided die?
Explanation
To find the probability of an event, we will use the following formula:
Now, given the event of rolling a factor of 5, we can calculate the following.
because there are 2 factors of 5 on a dice:
- 1
- 5
We can also calculate the following.
because there are 6 different possible numbers we can roll on a dice:
- 1
- 2
- 3
- 4
- 5
- 6
Knowing this, we can substitute into the formula. We get
Therefore, the probability of rolling a factor of 5 on a dice is .
The owner of a zoo wants to find out which animal exhibit is the most popular. The owner decided to take a random sample of the zoo's visitors to find out which exhibit was the visitor's favorite. Out of the visitors of the zoo last Friday, the owner asked
visitors which exhibit was their favorite. The results are shown in the provided table.
What inference can be made based on the results shown in the provided table?
The Panda Exhibit and the Gorilla Exhibit are the top two most popular exhibits
The Panda Exhibit and the Gibbons Exhibit are the top two most popular exhibits
The Gorilla Exhibit and the Gibbons Exhibit are the top two most popular exhibits
No inference can be made based on this data
Explanation
We can use data from a random sample to make inferences about a population. In this case, our population is all of the visitors of the zoo on Friday, and the random sample is the visitors that were randomly selected by the owner and asked which exhibit was their favorite.
Based on our answer choices, we are making an inference about which two animal exhibits are the most popular. The pandas received the most votes out of the owner's pole, followed by the gorillas; thus, we can infer—based on these results—that the Panda Exhibit and the Gorilla Exhibit are the two most popular exhibits at the zoo.
A cell phone company wanted to find out what brand of phones their customers use. Select the option that best represents a population.
All of the cell phone company's customers
The entire population in the United States
A random sample of the cell phone company's customers
The entire population in Texas
Explanation
In order to answer this question we first need to know what "population" means. A population is the entire group that is being studied, in this case all of the customers of the cell phone company.
"The entire population in the United States" and "The entire population in Texas" are not the correct answer because not everyone in an entire population uses the same cell phone company, and this company is only concerned about their own customers. Also, a random sample does not represent a population, so that is not the correct answer.
After a school debate by the students running for student council, the principal wanted to know what the student body thought about the topics that were debated. Select the option that best represents a sample.
Everyone who was at the debate
All of the teachers
The girls that attend the school
A random selection of the students who were at the debate
Explanation
In order to answer this question we first need to know what "sample" means. A sample is a subset of a population.
Because we want a subset, we don't want the entire population, which eliminates the answer choices "Everyone who was at the debate ". Also, the principal wants to know what the student body thought about the topics debated, not the teachers, which eliminates "All of the teachers". Finally, the principal didn't specify if she wanted just the girls' opinions, which makes "A random sample of the students who were at the debate" the best answer choice.
A bag contains red marbles,
pink marbles, and
purple marbles. What is the probability of not choosing a purple marble?
Explanation
The probability (p) is equal to the number of a specific event (purple marbles) divided by the total number of events. The probability of NOT p (called q) is equal to In this example:
In a dice game, what is the probability of rolling a factor of 5 on a six-sided die?
Explanation
To find the probability of an event, we will use the following formula:
Now, given the event of rolling a factor of 5, we can calculate the following.
because there are 2 factors of 5 on a dice:
- 1
- 5
We can also calculate the following.
because there are 6 different possible numbers we can roll on a dice:
- 1
- 2
- 3
- 4
- 5
- 6
Knowing this, we can substitute into the formula. We get
Therefore, the probability of rolling a factor of 5 on a dice is .
After a school choir concert, the music teacher wanted to know what the student body thought about the song choices. Select the option that best represents a sample.
Everyone who was at the choir concert
All of the teachers
The girls that attend the school
A random selection of the students who were at the concert
Explanation
In order to answer this question we first need to know what "sample" means. A sample is a subset of a population.
Because we want a subset, we don't want the entire population, which eliminates the answer choice "Everyone who was at the choir concert ". Also, the teacher wants to know what the student body thought about the songs, not the teachers, which eliminates "All of the teachers". Finally, the music teacher didn't specify if she wanted just the girls' opinions, which makes "A random sample of the students who were at the concert" the best answer choice.
A cell phone company wanted to find out what brand of phones their customers use. Select the option that best represents a population.
All of the cell phone company's customers
The entire population in the United States
A random sample of the cell phone company's customers
The entire population in Texas
Explanation
In order to answer this question we first need to know what "population" means. A population is the entire group that is being studied, in this case all of the customers of the cell phone company.
"The entire population in the United States" and "The entire population in Texas" are not the correct answer because not everyone in an entire population uses the same cell phone company, and this company is only concerned about their own customers. Also, a random sample does not represent a population, so that is not the correct answer.