questions 2a,b,c,d,e
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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questions 2a,b,c,d,e
questions 3a,b,c,d,e
question 4a,b,c,d,e,f
Transcribed Image Text:# Educational Exercise on Data Analysis and Line of Best Fit
## Army Drill Sergeants' Hundred-Meter Times
**Context**:
The scatterplot included shows the ages, \( a \), of 10 army drill sergeants and the time, \( T \), it took each to run 100 meters, measured in seconds.
### Questions:
a. **Hundred-meter time for the 25-year-old drill sergeant**:
- Observing the graph, locate the data point where age \( a \) is 25 and note the corresponding \( T \).
b. **Age of the drill sergeant with a 12.6-second time**:
- Find the point where \( T \) is 12.6 seconds and determine the age \( a \).
c. **Draw a line of best fit**:
- Analyze the scatterplot, visualizing a line that best represents the data distribution.
d. **Find the equation of your line of best fit**:
- Select two points on the line to calculate the equation using the slope-intercept formula \( y = mx + b \).
e. **Predictive Analysis**:
- Use the derived equation to predict the hundred-meter times for drill sergeants aged 40 and 12. Evaluate the reasonableness of these predictions.
## Birds' Nests and Predator Probability
**Context**:
Birds' nests face predation threats. The proximity of other nests increases this risk. Data below relates the probability of a nest being found by predators to the distance to the nearest neighboring nest (Perrins, 1979).
### Data:
| Distance to nearest neighbor (meters), \( d \) | 20 | 40 | 60 | 80 | 100 |
|------------------------------------------------|----|----|----|----|-----|
| Probability of predators (%), \( p \) | 47 | 34 | 32 | 17 | 1.5 |
### Questions:
a. **Plot and Best Fit Line**:
- Graph the data and draw a line best fitting the plotted points.
b. **Equation of the Line**:
- Use two points from your plotted line to ascertain the line's equation.
c. **Estimate Probability**:
- Using the equation, estimate the probability for nests with nearest neighbors located 50 meters away.
d. **Determining Distance for a Given Probability**:
- Determine the distance
b. 
c. 
d. 
2. The number of manatees killed by watercraft in Florida waters, \( n \), has been increasing since 1975. Let \( t \) be years since 1975. Data are given at 5-year intervals in the table. (Source: Florida Fish and Wildlife Conservation Commission)
| Year | Manatee deaths |
|------|----------------|
| 1975 | 6 |
| 1980 | 16 |
| 1985 | 33 |
| 1990 | 47 |
| 1995 | 42 |
| 2000 | 78 |
![Manatee deaths by Watercraft Graph]
a. Plot the points given in the table.
b. Draw a line of best fit.
c. Choose two points on your line to find the equation of your line of best fit for \( n \) in terms of \( t \).
d. Use the regression equation to estimate the number of manatees killed by watercraft in 1998.
e. Use the regression equation to estimate the number of manatees killed by watercraft in 2020. Comment on the accuracy of this estimate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd79997bd-1e0d-4ad8-8866-a9892cc695a2%2F94ae2333-2d97-4bfd-afe8-da803ef57ef5%2F56air1_processed.png&w=3840&q=75)
Transcribed Image Text:**Complete this assignment in the packet.**
1. Each line of best fit can be improved by adjusting the line. Draw a line that fits the data points more closely.
a. 
b. 
c. 
d. 
2. The number of manatees killed by watercraft in Florida waters, \( n \), has been increasing since 1975. Let \( t \) be years since 1975. Data are given at 5-year intervals in the table. (Source: Florida Fish and Wildlife Conservation Commission)
| Year | Manatee deaths |
|------|----------------|
| 1975 | 6 |
| 1980 | 16 |
| 1985 | 33 |
| 1990 | 47 |
| 1995 | 42 |
| 2000 | 78 |
![Manatee deaths by Watercraft Graph]
a. Plot the points given in the table.
b. Draw a line of best fit.
c. Choose two points on your line to find the equation of your line of best fit for \( n \) in terms of \( t \).
d. Use the regression equation to estimate the number of manatees killed by watercraft in 1998.
e. Use the regression equation to estimate the number of manatees killed by watercraft in 2020. Comment on the accuracy of this estimate.
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