A group of students were surveyed to find out if they like watching television or reading during their free time. The results of the survey are shown below:
90 students like watching television
20 students like watching television but do not like reading
80 students like reading
40 students do not like watching television
Make a two-way table to represent the data and use the table to answer the following questions.
Part A: What percentage of the total students surveyed like both watching television and reading? Show your work. (5 points)
Part B: What is the probability that a student who does not like watching television also does not like reading? Explain your answer. (5 points)
A two-way table representing the data:
| | Watching TV | Not Watching TV | Total |
|--------------|-------------|-----------------|-------|
| Reading | 20 | 60 | 80 |
| Not Reading | 70 | 40 | 110 |
| Total | 90 | 100 | 190 |
Part A:
Percentage of total students surveyed who like both watching television and reading:
= (Number of students who like both watching TV and reading / Total number of students surveyed) * 100
= (20 / 190) * 100
= 10.53%
Part B:
The probability that a student who does not like watching television also does not like reading can be calculated by considering only the "Not Watching TV" row:
= (Number of students who do not like watching TV and do not like reading) / (Number of students who do not like watching TV)
= 60 / 100
= 0.6 or 60%
Therefore, there is a 60% probability that a student who does not like watching television also does not like reading.
The graph shows the relationship between the number of months different students practiced boxing and the number of matches they won:
The title of the graph is Boxing Matches. On x axis, the label is Number of Months of Practice. On y axis, the label is Number of Matches Won. The scale on the y axis is from 0 to 21 at increments of 3, and the scale on the x axis is from 0 to 12 at increments of 2. The points plotted on the graph are the ordered pairs 0, 3 and 1, 6 and 2, 7 and 3, 9 and 4, 11 and 5, 13 and 6, 14 and 7, 16 and 8, 17 and 9, 18 and 10,20. A straight line is drawn joining the ordered pairs 0, 4 and 2, 7.1 and 4, 11 and 6, 13.5 and 8, 17 and 10, 20.5.
Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points)
Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice. Show your work and include the points used to calculate the slope. (5 points)
Part A:
The y-intercept of the line of best fit is approximately 3. This represents the number of matches won when the number of months of practice is 0. In this context, it could represent the natural skill or initial talent of the boxer to win matches before any formal practice.
Part B:
To find the equation of the line of best fit in slope-intercept form, we first need to calculate the slope using two points on the line. Let's use the points (0, 4) and (2, 7):
Slope (m) = (y2 - y1) / (x2 - x1)
= (7 - 4) / (2 - 0)
= 3 / 2
= 1.5
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line, using point (0, 4):
y - y1 = m(x - x1)
y - 4 = 1.5(x - 0)
y = 1.5x + 4
Therefore, the equation for the line of best fit is y = 1.5x + 4.
To predict the number of matches that could be won after 13 months of practice, substitute x = 13 into the equation:
y = 1.5(13) + 4
y = 19.5 + 4
y = 23.5
Therefore, the predicted number of matches that could be won after 13 months of practice is approximately 23.5.
Meg plotted the graph below to show the relationship between the temperature of her city and the number of sweaters sold at a store:
Main title on the graph is Sweater Sale. Graph shows 0 to 30 on x axis at increments of 5 and 0 to 12 on y axis at increments of 1. The label on the x axis is Temperature in degree C, and the label on the y axis is Number of Sweaters Sold. Dots are made at the ordered pairs 0, 12 and 2.5, 10 and 2.5, 11 and 5, 10 and 7.5, 9 and 7.5, 10 and 10, 7 and 12.5, 6 and 12.5, 8 and 15, 4 and 15, 7 and 17.5, 5 and 20, 1 and 20, 3 and 22.5, 9 and 25, 1 and 27.5, 1.
Part A: In your own words, describe the relationship between the temperature of the city and the sale of sweaters in the city. (5 points)
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)
Part A:
The relationship between the temperature of the city and the sale of sweaters based on the graph shows an inverse relationship. As the temperature increases, the number of sweaters sold decreases, and vice versa. This suggests that there is a negative correlation between temperature and sweater sales - when it gets warmer, fewer sweaters are sold, and when it gets colder, more sweaters are sold.
Part B:
To make the line of best fit, we need to calculate the slope and y-intercept using two points on the graph. Let's use the points (0, 12) and (5, 10) to calculate the slope:
Slope (m) = (y2 - y1) / (x2 - x1)
= (10 - 12) / (5 - 0)
= -2 / 5
= -0.4
Now, to find the y-intercept, we can use the equation of a line (y = mx + b) and substitute the slope and one of the points into the equation. Let's use the point (0, 12):
12 = -0.4(0) + b
b = 12
Therefore, the equation for the line of best fit is y = -0.4x + 12. The approximate slope is -0.4 and the y-intercept is 12. This line of best fit represents the overall trend of the relationship between temperature and sweater sales.
The scatter plot shows the relationship between the test scores of a group of students and the number of hours they play computer games in a week:
On a grid, Label Hours Playing Computer Games on x axis and Test Scores on y axis. The title of the graph is Test Scores and Computer Games. The scale on the x axis shows the numbers from 0 to 10 at increments of 1, and the scale on the y axis shows numbers from 0 to 100 at increments of 10. Dots are made at the ordered pairs 0, 90 and 0, 100 and 0.5, 89 and 1, 81 and 1, 95 and 1, 100 and 1.1, 85 and 2, 90 and 3, 81 and 3.5, 65 and 3.5, 75 and 5, 70 and 6, 55 and 6.5, 65 and 7, 52 and 7.5, 95 and 9, 65. The ordered pair 7.5, 95 is circled and labeled as B. All the other points are put in an oval and labeled as A.
Part A: What is the group of points labeled A called? What is the point labeled B called? Give a possible reason for the presence of point B. (5 points)
Part B: Describe the association between students' test scores and the number of hours they play computer games. (5 points)
Part A:
The group of points labeled A is called a cluster or a set of data points. These points represent a pattern or trend in the relationship between the number of hours playing computer games and test scores. The point labeled B is called an outlier. Outliers are data points that significantly differ from the rest of the data and do not follow the general pattern or trend of the data.
One possible reason for the presence of point B could be that this particular student may have unique circumstances or characteristics that affect their test score and playing time. For example, the student could have exceptional problem-solving skills honed through playing complex computer games, resulting in a high test score despite spending a significant amount of time on gaming.
Part B:
The association between students' test scores and the number of hours they play computer games based on the scatter plot shows a generally negative relationship. As the number of hours playing computer games increases, the test scores tend to decrease. This negative association indicates that spending more time playing computer games may have a negative impact on the students' test scores. However, there are variations among students, as shown by the outlier point B, suggesting that other factors may influence the relationship between test scores and gaming hours.