1.
Before an election, 5,000 voters were asked for their preferences. One thousand two hundred (1,200) said they would vote for Candidate A; 3,000 preferred Candidate B; and the rest were undecided. What is the relative frequency of undecided voters? Express the answer in decimal form.
0.84
0.16
800
0.27
The total number of voters who were surveyed is 5,000.
Out of those 5,000 voters, 1,200 said they would vote for Candidate A, and 3,000 preferred Candidate B.
To find the number of undecided voters, we can subtract the number of voters who have made a decision from the total number of voters:
Undecided voters = Total voters - (Candidate A voters + Candidate B voters)
Undecided voters = 5,000 - (1,200 + 3,000)
Undecided voters = 800
So there are 800 undecided voters.
To find the relative frequency of undecided voters, we need to divide the number of undecided voters by the total number of voters:
Relative frequency of undecided voters = Undecided voters / Total voters
Relative frequency of undecided voters = 800 / 5,000
Relative frequency of undecided voters = 0.16
Therefore, the relative frequency of undecided voters is 0.16, or 16% (expressed as a percentage).
The answer is: 0.16.
You want to estimate the number of students who bring their lunch to school every day. Which of the following is the best sample for this situation?(1 point)
Responses
50 female students selected at random
50 female students selected at random
all members of the Math Club
all members of the Math Club
80 students selected at random during lunch
80 students selected at random during lunch
45 first-year students selected at random
45 first-year students selected at random
A coffee shop owner is interested in determining what people think about the new coffee flavor. Which of the following is the population in this situation?(1 point)
Responses
100 random customers
100 random customers
the first 50 customers who bought the new coffee
the first 50 customers who bought the new coffee
all customers who bought the new coffee
all customers who bought the new coffee
all customers who did not buy the new coffee
all customers who did not buy the new coffee
Tom wants to know the average number of musical instruments students in his school play. He used the school’s two band classes, consisting of a total of 48 students, as his representative sample. He concluded that students in his school play an average of three musical instruments. Is his conclusion valid?(1 point)
Responses
No, because his representative sample is too large.
No, because his representative sample is too large.
Yes, because all members of the sample play at least one musical instrument.
Yes, because all members of the sample play at least one musical instrument.
No, because he did not choose students randomly.
No, because he did not choose students randomly.
Yes, because the sample includes both males and females who play musical instruments.
A survey is conducted to determine the most common reason people own a cell phone. A company sent out a survey to customers between the ages of 20 and 30. Based on the responses, the company concluded that people own a cell phone for messaging purposes. Is this conclusion valid?(1 point)
Responses
Yes, because the sample includes male and female customers.
Yes, because the sample includes male and female customers.
No, because not all people who own a cell phone have the same probability of being selected.
No, because not all people who own a cell phone have the same probability of being selected.
No, because the sample includes customers of too many different ages.
No, because the sample includes customers of too many different ages.
Yes, because the sample includes all customers between the ages of 20 and 30.
Yes, because the sample includes all customers between the ages of 20 and 30.
A school principal wants to know the average number of extracurricular activities students in her school are involved in. She assigned each student a number from 1 to 415. Using a random number generator, she selected 200 students to be part of the sample. She concluded that students are involved in an average of two extracurricular activities. Is the principal’s conclusion valid?(1 point)
Responses
Yes, because every student had an equal chance to be part of the sample. The sample size also appears to be large enough.
Yes, because every student had an equal chance to be part of the sample. The sample size also appears to be large enough.
No, because 200 students in the sample is too large.
No, because 200 students in the sample is too large.
No, because not all students in the sample have extracurricular activities.
No, because not all students in the sample have extracurricular activities.
Yes, because only those who have extracurricular activities were included in the sample.
Yes, because only those who have extracurricular activities were included in the sample.
To find the relative frequency of undecided voters, we need to determine the number of voters who are undecided out of the total number of voters.
Given that 5,000 voters were asked for their preferences and the number of voters who prefer Candidate A and Candidate B, we can calculate the number of undecided voters by subtracting the sum of those two from the total number of voters.
Number of undecided voters = Total voters - (Number of voters for Candidate A + Number of voters for Candidate B)
Number of undecided voters = 5,000 - (1,200 + 3,000)
Number of undecided voters = 5,000 - 4,200
Number of undecided voters = 800
To find the relative frequency, we need to divide the number of undecided voters by the total number of voters:
Relative frequency of undecided voters = Number of undecided voters / Total voters
Relative frequency of undecided voters = 800 / 5,000
Relative frequency of undecided voters ≈ 0.16
Therefore, the relative frequency of undecided voters, expressed in decimal form, is 0.16.
The best sample for estimating the number of students who bring their lunch to school every day is:
80 students selected at random during lunch.
The population in the situation where a coffee shop owner wants to determine what people think about the new coffee flavor is:
All customers who bought the new coffee.
Tom's conclusion about the average number of musical instruments students in his school play is not valid because:
He did not choose students randomly.
The conclusion that people own a cell phone for messaging purposes based on a survey sent out to customers between the ages of 20 and 30 is not valid because:
Not all people who own a cell phone have the same probability of being selected.
The principal's conclusion about the average number of extracurricular activities students in her school are involved in is valid because:
Every student had an equal chance to be part of the sample. The sample size also appears to be large enough.