Suppose the value of Young's modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations. 116.6 115.5 114.7 115.2 115.9 (a) Calculate x (in GPa). GPa Calculate the deviations from the mean. 116.6 115.5 114.7 115.2 115.9 deviation (b) Use the deviations calculated in part (a) to obtain the sample variance (in GP22). s2 = | GPa? Use the deviations calculated in part (a) to obtain the sample standard deviation (in GPa). (Round your answer to three decimal places.) S = GPa
Suppose the value of Young's modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations. 116.6 115.5 114.7 115.2 115.9 (a) Calculate x (in GPa). GPa Calculate the deviations from the mean. 116.6 115.5 114.7 115.2 115.9 deviation (b) Use the deviations calculated in part (a) to obtain the sample variance (in GP22). s2 = | GPa? Use the deviations calculated in part (a) to obtain the sample standard deviation (in GPa). (Round your answer to three decimal places.) S = GPa
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...
Related questions
Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
100%
Please solve (a) & (b) only!
![**Young’s Modulus Calculations**
Suppose the value of Young's modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations:
- 116.6, 115.5, 114.7, 115.2, 115.9
### (a) Calculate the Sample Mean (\(\overline{x}\) in GPa).
\[ \text{Sample Mean } (\overline{x}) = \]
\[ \text{Deviation: Calculate the deviations from the mean.} \]
| \(x\) | 116.6 | 115.5 | 114.7 | 115.2 | 115.9 |
|-----------|-------|-------|-------|-------|-------|
| Deviation | | | | | |
### (b) Sample Variance and Standard Deviation
1. Use the deviations calculated in part (a) to obtain the sample variance (\(s^2\) in GPa²).
\[ s^2 = \]
2. Use the deviations calculated in part (a) to obtain the sample standard deviation (\(s\) in GPa). (Round your answer to three decimal places.)
\[ s = \]
### (c) Compute \(s^2\) Using Computational Formula
1. Calculate \(s^2\) (in GPa²) by using the computational formula for the numerator \(S_{xx}\).
\[ \text{GPa}^2 = \]
### (d) Transform Observations
1. Subtract 100 from each observation to obtain a sample of transformed values. Now calculate the sample variance (\(s^2\) in GPa²) of these transformed values.
\[ \text{GPa}^2 = \]
This exercise involves basic statistical techniques to analyze the variability and central tendency in a set of Young's modulus measurements.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F306db17a-c2a3-4020-aada-7a92dff91485%2Fb91302f5-d9e9-417d-95da-6375533b424d%2Fbp74ls_processed.png&w=3840&q=75)
Transcribed Image Text:**Young’s Modulus Calculations**
Suppose the value of Young's modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations:
- 116.6, 115.5, 114.7, 115.2, 115.9
### (a) Calculate the Sample Mean (\(\overline{x}\) in GPa).
\[ \text{Sample Mean } (\overline{x}) = \]
\[ \text{Deviation: Calculate the deviations from the mean.} \]
| \(x\) | 116.6 | 115.5 | 114.7 | 115.2 | 115.9 |
|-----------|-------|-------|-------|-------|-------|
| Deviation | | | | | |
### (b) Sample Variance and Standard Deviation
1. Use the deviations calculated in part (a) to obtain the sample variance (\(s^2\) in GPa²).
\[ s^2 = \]
2. Use the deviations calculated in part (a) to obtain the sample standard deviation (\(s\) in GPa). (Round your answer to three decimal places.)
\[ s = \]
### (c) Compute \(s^2\) Using Computational Formula
1. Calculate \(s^2\) (in GPa²) by using the computational formula for the numerator \(S_{xx}\).
\[ \text{GPa}^2 = \]
### (d) Transform Observations
1. Subtract 100 from each observation to obtain a sample of transformed values. Now calculate the sample variance (\(s^2\) in GPa²) of these transformed values.
\[ \text{GPa}^2 = \]
This exercise involves basic statistical techniques to analyze the variability and central tendency in a set of Young's modulus measurements.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON