Question

A pie chart divided into 6 inequal sections is titled Activity Hours per Week. The sections are labeled school, 40, 24 percent; eat, 21, 13 percent; sports or play, 15, 9 percent; social media or TV, 24, 14 percent; sleep, 56; and other 12, 7 percent.

The activity for one week of 168 people was tracked and displayed in a circle graph. What was the percentage of time spent on sleep? Round the percentage to the nearest whole number.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the percentage of time spent on sleep, we first need to find the total number of hours spent on all activities. Adding up the hours in each section:

40 (school) + 21 (eat) + 15 (sports or play) + 24 (social media or TV) + 56 (sleep) + 12 (other) = 168

So, the total number of hours spent in a week is 168.

Now, to find the percentage of time spent on sleep, we divide the number of hours spent on sleep by the total number of hours and multiply by 100:

(56/168) * 100 = 33.33%

Rounded to the nearest whole number, the percentage of time spent on sleep is 33%.

Answer 2

A hotel maintenance crew wants to estimate how many of the 12,000 lamps in their 30-story hotel need a new light bulb. Which of the following is a random sample of lamps to be inspected?(1 point)

Responses

all lamps from the rooms with king-sized beds
all lamps from the rooms with king-sized beds

100 lamps on each floor chosen randomly
100 lamps on each floor chosen randomly

400 lamps on the first 10 floors
400 lamps on the first 10 floors

all lamps in booked rooms
all lamps in booked rooms

Answer 3

[AI-generated answer — Bot GPT 3.5]

100 lamps on each floor chosen randomly

This option represents a random sample because it involves selecting a random sample of lamps from each floor of the hotel. This method ensures that a representative sample of lamps from various areas of the hotel is inspected, providing a more accurate estimate of how many lamps need a new light bulb throughout the hotel.

Answer 4

A local library manager randomly surveys 80 patrons about the type of book they borrow when they visit the library. The manager finds that 3 patrons borrow novels. If the local library has 345 patrons, approximately how many of them borrow novels when they visit the library? Round your answer to the nearest whole number. (1 point)

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the approximate number of patrons who borrow novels when they visit the library, we can set up a proportion using the information given in the survey:

Number of patrons who borrow novels / Total number of surveyed patrons = Number of patrons who borrow novels in the entire library / Total number of patrons in the library

Let x be the number of patrons who borrow novels in the entire library.

3 (number of patrons who borrow novels in the survey) / 80 (total surveyed patrons) = x / 345 (total patrons in the library)

Cross multiply to solve for x:

3 * 345 = 80 * x
1035 = 80x

x = 1035 / 80
x ≈ 12.94

Rounded to the nearest whole number, approximately 13 patrons borrow novels when they visit the library.

Answer 6

Use the table to answer the question.

Group A 18 20 46 34 58 31 41
Group B 15 21 32 42 29 57 39
The table shows the times, in minutes, spent shopping by two different groups. First find the mean times each group spent shopping. Then determine the difference in the mean times. Round your answers to one decimal place.(2 points)

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the mean time each group spent shopping, we first calculate the sum of times in each group and then divide by the number of values in the group.

For Group A:
Sum of times = 18 + 20 + 46 + 34 + 58 + 31 + 41 = 228
Number of values = 7
Mean time for Group A = 228 / 7 ≈ 32.6 minutes

For Group B:
Sum of times = 15 + 21 + 32 + 42 + 29 + 57 + 39 = 235
Number of values = 7
Mean time for Group B = 235 / 7 ≈ 33.6 minutes

To find the difference in the mean times:
Difference = Mean time for Group B - Mean time for Group A
Difference = 33.6 - 32.6
Difference ≈ 1.0 minutes

Therefore, the mean time for Group A is approximately 32.6 minutes, the mean time for Group B is approximately 33.6 minutes, and the difference in mean times is approximately 1.0 minutes.

Answer 8

i think group a is 34.5 mins and group b is 33.6 mins

Answer 9

[AI-generated answer — Bot GPT 3.5]

Let's recalculate the mean times for each group and determine the difference:

For Group A:
Sum of times = 18 + 20 + 46 + 34 + 58 + 31 + 41 = 228
Number of values = 7
Mean time for Group A = 228 / 7 ≈ 32.6 minutes

For Group B:
Sum of times = 15 + 21 + 32 + 42 + 29 + 57 + 39 = 235
Number of values = 7
Mean time for Group B = 235 / 7 ≈ 33.6 minutes

The mean time for Group A is indeed approximately 32.6 minutes and for Group B is approximately 33.6 minutes.

To determine the difference in mean times:
Difference = Mean time for Group B - Mean time for Group A
Difference = 33.6 - 32.6
Difference = 1.0 minute

Therefore, the mean time for Group A is indeed approximately 32.6 minutes, the mean time for Group B is approximately 33.6 minutes, and the difference in mean times is indeed 1.0 minute. Thank you for pointing out the discrepancy.

Answer 10

Which data set has the highest median?(1 point)

Responses

{1, 6, 15, 7, 15, 18, 14}
left brace 1 comma 6 comma 15 comma 7 comma 15 comma 18 comma 14 right brace

{1, 10, 8, 29, 14, 17, 3}
left brace 1 comma 10 comma 8 comma 29 comma 14 comma 17 comma 3 right brace

{8, 20, 13, 14, 12, 9}
left brace 8 comma 20 comma 13 comma 14 comma 12 comma 9 right brace

{11, 15, 16, 8, 12, 14}

Answer 11

[AI-generated answer — Bot GPT 3.5]

To determine which data set has the highest median, we need to find the median of each data set and compare them.

1. For the data set {1, 6, 15, 7, 15, 18, 14}:
- First, we need to reorder the data in ascending order: {1, 6, 7, 14, 15, 15, 18}
- The median is the middle value when the data set is ordered, or the average of the two middle values if the data set has an even number of values. In this case, the median is 14.

2. For the data set {1, 10, 8, 29, 14, 17, 3}:
- First, we need to reorder the data in ascending order: {1, 3, 8, 10, 14, 17, 29}
- The median is the middle value when the data set is ordered. In this case, the median is 10.

3. For the data set {8, 20, 13, 14, 12, 9}:
- First, we need to reorder the data in ascending order: {8, 9, 12, 13, 14, 20}
- The median is the middle value when the data set is ordered, or the average of the two middle values if the data set has an even number of values. In this case, the median is 13.5.

4. For the data set {11, 15, 16, 8, 12, 14}:
- First, we need to reorder the data in ascending order: {8, 11, 12, 14, 15, 16}
- The median is the middle value when the data set is ordered, or the average of the two middle values if the data set has an even number of values. In this case, the median is 13.5.

Therefore, the data set {1, 6, 15, 7, 15, 18, 14} has the highest median, which is 14.

Answer 12

Theo, Ara, Jose, and Dana all got 100 percent on their latest math test. Their scores on the previous six tests are listed. Whose mean test score will increase the most? (1 point)

Responses

Ara: 100, 98, 99, 97, 100, 100
Ara: 100, 98, 99, 97, 100, 100

Dana: 68, 74, 83, 80, 81, 82
Dana: 68, 74, 83, 80, 81, 82

Theo: 84, 88, 81, 85, 77, 76
Theo: 84, 88, 81, 85, 77, 76

Jose: 91, 93, 97, 96, 96, 96

Answer 13

[AI-generated answer — Bot GPT 3.5]

To determine whose mean test score will increase the most, we can calculate the mean test score for each student for the first six tests, then calculate the new mean including their latest perfect test score, and compare the increase in their mean score.

First, let's calculate the mean test scores for the first six tests for each student:

Ara:
(100 + 98 + 99 + 97 + 100 + 100) / 6 = 99

Dana:
(68 + 74 + 83 + 80 + 81 + 82) / 6 ≈ 78

Theo:
(84 + 88 + 81 + 85 + 77 + 76) / 6 ≈ 81.8

Jose:
(91 + 93 + 97 + 96 + 96 + 96) / 6 ≈ 95.5

Now, let's calculate the new mean test scores including their perfect test score:

Ara:
(99 + 100) / 2 = 99.5

Dana:
(78 + 100) / 2 = 89

Theo:
(81.8 + 100) / 2 ≈ 90.9

Jose:
(95.5 + 100) / 2 = 97.75

The difference in mean scores for each student after the perfect test score:

- Ara: 99.5 - 99 = 0.5
- Dana: 89 - 78 = 11
- Theo: 90.9 - 81.8 = 9.1
- Jose: 97.75 - 95.5 = 2.25

Therefore, Dana's mean test score will increase the most, with an increase of 11 points.

Answer 14

Statistics Unit Test

9 of 159 of 15 Items

Question
The stem-and-leaf plot shows the speeds of the fastest steel roller coasters in Europe. The table shows the speeds of the fastest steel roller coasters in North America.

Speeds of the Fastest Steel Roller Coasters in Europe (in miles per hour)

Stem Leaf
7 4 5 5 5
8 0 0 3 4 8
9 9
11 1Key: 7|4=74 miles per hour

Speeds of the Fastest Steel Roller Coasters in North America (in miles per hour)

Canada 90 128 91
U.S. 93 120 100
Mexico 95 92 85
Find the range of the speeds of the fastest steel roller coasters on both continents.

(1 point)

Answer 15

[AI-generated answer — Bot GPT 3.5]

To find the range of the speeds of the fastest steel roller coasters on both continents, we need to find the difference between the highest and lowest speeds.

For Europe:
The highest speed in Europe is the highest leaf in the stem-and-leaf plot, which is 91 mph.
The lowest speed in Europe is the lowest leaf in the stem-and-leaf plot, which is 34 mph.

Range in Europe: 91 mph - 34 mph = 57 mph

For North America:
The highest speed in North America is 128 mph (from Canada).
The lowest speed in North America is 85 mph (from Mexico).

Range in North America: 128 mph - 85 mph = 43 mph

Therefore, the ranges of the speeds of the fastest steel roller coasters in Europe and North America are 57 mph and 43 mph, respectively.

Answer 16

Statistics Unit Test

11 of 1511 of 15 Items

Question
These are the scores for two randomly selected lacrosse teams. Find the range of the number of goals scored by each team. Based on the range, which team has a more consistent number of goals scored?

Lacrosse Team 1: 6 0 4 17 3 12
Lacrosse Team 2: 23 14 22 14 17 22

Answer 17

[AI-generated answer — Bot GPT 3.5]

To find the range of the number of goals scored by each team, we need to calculate the difference between the highest and lowest scores for each team.

For Lacrosse Team 1:
The highest score is 17.
The lowest score is 0.
Range for Team 1: 17 - 0 = 17

For Lacrosse Team 2:
The highest score is 23.
The lowest score is 14.
Range for Team 2: 23 - 14 = 9

Based on the range, Team 2 has a more consistent number of goals scored because its range is smaller (9) compared to Team 1's range (17). A smaller range indicates less variability in the number of goals scored, making the scoring more consistent for Team 2.

Answer 18

An illustration shows two sets of dot plots. One is titled Gas Mileage in miles per gallon, Cars and the other is Gas Mileage in miles per gallon, S U Vs. The plots are shown as dots in a vertical row over each number on a number line. For Cars, a number line with arrows on both ends ranges from 18 to 22 in increments of 1. There is 1 dot above 18, 2 dots above 19, 3 dots above 20, 2 dots above 21, and 1 dot above 22. For S U Vs, a number line with arrows on both ends ranges from 21 to 25 in increments of 1. There is 1 dot above 21, 1 dot above 22, 2 dots above 23, 2 dots above 24, and 3 dots above 25.

The dot plots show the gas mileage for randomly selected cars and SUVs. Which data values do both distributions have in common?
The data value in common for both distributions with the lowest number is
.

The data value in common for both distributions for the highest number is
.

Answer 19

[AI-generated answer — Bot GPT 3.5]

To find the data values that both distributions have in common, we can look at the overlapping values between the two dot plots.

For Cars:
The range is from 18 to 22, with frequencies 1, 2, 3, 2, and 1.

For S U Vs:
The range is from 21 to 25, with frequencies 1, 1, 2, 2, and 3.

To determine the data values in common:

The lowest value in the range where both have data points is 21, as both distributions have a dot above this value.

The highest value in the range where both have data points is 22, as both distributions have a dot above this value.

Therefore, the data value in common for both distributions with the lowest number is 21 and the data value in common for both distributions with the highest number is 22.

Answer 20

Fifteen students are randomly selected from two different classes. They were asked how many books they read during the summer. Their responses are as follows. Find the median number of books read by each class. Which class has a higher median number of books read?

Class 1: 0, 5, 3, 6, 7, 8, 10, 1, 1, 4, 5, 6, 4, 5, 6
Class 2: 2, 2, 4, 3, 0, 0, 6, 7, 10, 9, 6, 5, 3, 1, 2

Answer 21

[AI-generated answer — Bot GPT 3.5]

To find the median number of books read by each class and determine which class has a higher median number of books read, we need to arrange the data in each class in ascending order and find the middle value (or average of the two middle values if the sample size is even).

For Class 1:
0, 1, 1, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 10

There are 15 students, so the median is the 8th value:
Median for Class 1 = 5

For Class 2:
0, 0, 1, 2, 2, 2, 3, 3, 4, 5, 6, 6, 7, 9, 10

There are 15 students, so the median is the 8th value:
Median for Class 2 = 3

Therefore, Class 1 has a higher median number of books read, with a median of 5 compared to Class 2's median of 3.

Answer 22

Maritza plays in a softball league. She wants to know about how many players in the league also play basketball. Because there are 225 players in the league, she chooses the names of 45 of the players and asks them whether they also play basketball. Describe the population and the sample. What is the size of the population, and what is the size of the sample? Show your work.(2 points)

Answer 23

[AI-generated answer — Bot GPT 3.5]

Population and Sample:

- Population: The entire group of interest, in this case, all the players in the softball league. Maritza wants to know about how many players in the league also play basketball.
- Sample: A subset of the population, in this case, the 45 players whom Maritza has chosen to survey about whether they also play basketball.

Size of the Population and Sample:

- Size of the Population: There are 225 players in the softball league. This is the total number of players in the population.
- Size of the Sample: Maritza chooses 45 players from the entire softball league to survey about playing basketball. This is the size of the sample selected for the survey.

Therefore:
- Size of the population: 225 players
- Size of the sample: 45 players

The population size refers to the total number of individuals in the group being studied, while the sample size represents the number of individuals selected for data collection from the population.