(d) What is the probability that the observed depth is within 1 standard deviation of the mean value? (Round your answer to four decimal places.)What is the probability that the observed depth is within 2 standard deviations of the mean value? An article suggests the uniform distribution on the interval \( (8.5, 19) \) 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: 13.75 ✅- Variance: 9.1875 ✅**(b) What is the cdf of depth?**\[ F(x) = \begin{cases} 0 & x < 8.5 \\ \frac{x - 8.5}{10.5} & 8.5 \leq x < 19 \\ 1 & 19 \leq x \end{cases} \] ✅**(c) What is the probability that observed depth is at most 10? (Round your answer to four decimal places.)**- Probability: 0.1429 ✅What is the probability that observed depth is between 10 and 15? (Round your answer to four decimal places.)- Probability: 0.4762 ✅**(d) What is the probability that the observed depth is within 1 standard deviation of the mean value? (Round your answer to four decimal places.)**What is the probability that the observed depth is within 2 standard deviations of the mean value?

Given Cdf F(x)=0 when x<8.5 F(x)=(x-8.5)/10.5 8.5≤x≤19 F(X)=1 x≥19

Answered: (d) What is the probability that the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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

What is the probability that the observed depth is within 2 standard deviations of the mean value?

An article suggests the uniform distribution on the interval \( (8.5, 19) \) 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: 13.75 ✅
- Variance: 9.1875 ✅

**(b) What is the cdf of depth?**
\[
F(x) =
\begin{cases}
0 & x < 8.5 \\
\frac{x - 8.5}{10.5} & 8.5 \leq x < 19 \\
1 & 19 \leq x
\end{cases}
\]
✅

**(c) What is the probability that observed depth is at most 10? (Round your answer to four decimal places.)**
- Probability: 0.1429 ✅

What is the probability that observed depth is between 10 and 15? (Round your answer to four decimal places.)
- Probability: 0.4762 ✅

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

What is the probability that the observed depth is within 2 standard deviations of the mean value?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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