**Uniform Distribution Model for Sediment Depth**An article suggests using the uniform distribution on the interval (6.5, 21) as a model for the depth (in cm) of the bioturbation layer in sediment in a certain region.**(a) Mean and Variance of Depth**- Mean: ________- Variance: ________ (Round your variance to two decimal places.)**(b) Cumulative Distribution Function (CDF) of Depth**The CDF, $ F(x) $, is defined as:\[F(x) = \begin{cases} 0 & x < 6.5 \\\frac{x - 6.5}{14.5} & 6.5 \le x < 21 \\1 & 21 \le x\end{cases}\]**(c) Probability Calculations**- What is the probability that the observed depth is at most 10? (Round your answer to four decimal places.) - Probability: ________- What is the probability that the observed depth is between 10 and 15? (Round your answer to four decimal places.) - Probability: ________**(d) Standard Deviation Calculations**- What is the probability that the observed depth is within 1 standard deviation of the mean value? (Round your answer to four decimal places.) - Probability: ________- What is the probability that the observed depth is within 2 standard deviations of the mean value? - Probability: ________This information provides a mathematical framework for understanding the distribution of sediment depths using a uniform model in environmental studies.

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Description: **Uniform Distribution Model for Sediment Depth**An article suggests using the uniform distribution on the interval (6.5, 21) as a model for the depth (in cm) of the bioturbation layer in sediment in a certain region.**(a) Mean and Variance of Depth

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An article suggests the uniform distribution on the interval (6.5, 21) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. (a) What are the mean and variance of depth? (Round your variance to two decimal places.) mean variance (b) What is the cdf of depth? x< 6.5 F(x) = 6.5 sx< 21 1 21 sx (c) What is the probability that observed depth is at most 10? (Round your answer to four decimal places.) What is the probability that observed depth is between 10 and 15? (Round your answer to four decimal places.)

An article suggests the uniform distribution on the interval (6.5, 21) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. (a) What are the mean and variance of depth? (Round your variance to two decimal places.) mean variance (b) What is the cdf of depth? x< 6.5 F(x) = 6.5 sx< 21 1 21 sx (c) What is the probability that observed depth is at most 10? (Round your answer to four decimal places.) What is the probability that observed depth is between 10 and 15? (Round your answer to four decimal places.)

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Question

**Uniform Distribution Model for Sediment Depth**

An article suggests using the uniform distribution on the interval (6.5, 21) as a model for the depth (in cm) of the bioturbation layer in sediment in a certain region.

**(a) Mean and Variance of Depth**

- Mean: ________
- Variance: ________ (Round your variance to two decimal places.)

**(b) Cumulative Distribution Function (CDF) of Depth**

The CDF, $ F(x) $, is defined as:

\[
F(x) =
\begin{cases}
0 & x < 6.5 \\
\frac{x - 6.5}{14.5} & 6.5 \le x < 21 \\
1 & 21 \le x
\end{cases}
\]

**(c) Probability Calculations**

- What is the probability that the observed depth is at most 10? (Round your answer to four decimal places.)
- Probability: ________

- What is the probability that the observed depth is between 10 and 15? (Round your answer to four decimal places.)
- Probability: ________

**(d) Standard Deviation Calculations**

- What is the probability that the observed depth is within 1 standard deviation of the mean value? (Round your answer to four decimal places.)
- Probability: ________

- What is the probability that the observed depth is within 2 standard deviations of the mean value?
- Probability: ________

This information provides a mathematical framework for understanding the distribution of sediment depths using a uniform model in environmental studies.

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