An article suggests the uniform distribution on the interval from 7.5 to 20 as a model for x = depth (in centimeters) of the bioturbation layer in sediment for a certain region. (a) Draw the density curve for x. Density 0.10 0.08 0.06 0.04 0.02 Density 0.10 0.08 0.06 0.04 8 0.02 8 10 10 12 12 14 14 (b) What is the height of the density curve? 16 18 16 18 (c) What is the probability that x is at most 12? P(x ≤ 12) = 20 لسبب 20 X Density 0.10 0.08 0.06 0.04 0.02 Density 0.10 0.08 0.06 0.04 8 0.02 8 10 10 12 14 16 18 2 12 14 16 18 2
An article suggests the uniform distribution on the interval from 7.5 to 20 as a model for x = depth (in centimeters) of the bioturbation layer in sediment for a certain region. (a) Draw the density curve for x. Density 0.10 0.08 0.06 0.04 0.02 Density 0.10 0.08 0.06 0.04 8 0.02 8 10 10 12 12 14 14 (b) What is the height of the density curve? 16 18 16 18 (c) What is the probability that x is at most 12? P(x ≤ 12) = 20 لسبب 20 X Density 0.10 0.08 0.06 0.04 0.02 Density 0.10 0.08 0.06 0.04 8 0.02 8 10 10 12 14 16 18 2 12 14 16 18 2
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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![**Uniform Distribution in Bioturbation Layer Depths**
An article suggests the uniform distribution on the interval from 7.5 to 20 as a model for \( x = \) depth (in centimeters) of the bioturbation layer in sediment for a certain region.
### (a) Draw the Density Curve for \( x \).
Four graphs are shown, each with the horizontal axis labeled from 8 to 20 and the vertical axis labeled "Density" from 0 to 0.10. Each graph depicts a different horizontal line representing the uniform distribution:
1. First graph: The line is at a height of 0.08.
2. Second graph: The line is at the height of 0.06.
3. Third graph: The line is at the height of 0.07.
4. Fourth graph: The line is at the height of 0.05.
Only one circle next to each graph can be selected to indicate the correct density curve.
### (b) What is the Height of the Density Curve?
This section provides a blank space for students to write the height of the correct density curve.
### (c) What is the Probability that \( x \) is at Most 12?
\[ P(x \leq 12) = \]
There is a blank space for students to compute and input the probability that \( x \) is at most 12.
### (d) What is the Probability that \( x \) is between 10 and 16?
\[ P(10 \leq x \leq 16) = \]
Another blank space is provided for students to calculate and enter the probability for this range.
### (e) What is the Probability that \( x \) is between 11 and 17?
\[ P(11 \leq x \leq 17) = \]
Students are expected to fill in the probability for this specified interval.
### (f) Why are the Two Probabilities Computed in Parts (d) and (e) Equal?
Students are presented with multiple-choice options to explain why the probabilities in parts (d) and (e) are equal:
- The two probabilities are equal because they are represented on the graph by rectangles of equal width and equal height.
- The two probabilities are equal because they begin at the same x-value.
- The two probabilities are equal because their midpoints are at the same x-value.
- The two probabilities are equal](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec13ab4f-5933-4c78-80c6-824491a34faa%2Fb885681b-ad86-43ac-9806-1158df21aa69%2Fveii679_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Uniform Distribution in Bioturbation Layer Depths**
An article suggests the uniform distribution on the interval from 7.5 to 20 as a model for \( x = \) depth (in centimeters) of the bioturbation layer in sediment for a certain region.
### (a) Draw the Density Curve for \( x \).
Four graphs are shown, each with the horizontal axis labeled from 8 to 20 and the vertical axis labeled "Density" from 0 to 0.10. Each graph depicts a different horizontal line representing the uniform distribution:
1. First graph: The line is at a height of 0.08.
2. Second graph: The line is at the height of 0.06.
3. Third graph: The line is at the height of 0.07.
4. Fourth graph: The line is at the height of 0.05.
Only one circle next to each graph can be selected to indicate the correct density curve.
### (b) What is the Height of the Density Curve?
This section provides a blank space for students to write the height of the correct density curve.
### (c) What is the Probability that \( x \) is at Most 12?
\[ P(x \leq 12) = \]
There is a blank space for students to compute and input the probability that \( x \) is at most 12.
### (d) What is the Probability that \( x \) is between 10 and 16?
\[ P(10 \leq x \leq 16) = \]
Another blank space is provided for students to calculate and enter the probability for this range.
### (e) What is the Probability that \( x \) is between 11 and 17?
\[ P(11 \leq x \leq 17) = \]
Students are expected to fill in the probability for this specified interval.
### (f) Why are the Two Probabilities Computed in Parts (d) and (e) Equal?
Students are presented with multiple-choice options to explain why the probabilities in parts (d) and (e) are equal:
- The two probabilities are equal because they are represented on the graph by rectangles of equal width and equal height.
- The two probabilities are equal because they begin at the same x-value.
- The two probabilities are equal because their midpoints are at the same x-value.
- The two probabilities are equal
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