The shear strength of each of ten test spot welds is determined, yielding the following data (psi). 367 362 415 358 367 373 409 387 389 375 (a) Assuming that shear strength is normally distributed, estimate the true average shear strength and standard deviation of shear strength using the method of maximum likelihood. (Round your answers to two decimal places.) average standard deviation psi psi (b) Again assuming a normal distribution, estimate the strength value below which 95% of all welds will have their strengths. [Hint: What is the 95th percentile in terms of u and o? Now use the invariance principle.] (Round your answer to two decimal places.) psi (c) Suppose we decide to examine another test spot weld. Let X = shear strength of the weld. Use the given data to obtain the mle of P(X ≤ 400). [Hint: P(X ≤ 400) = ((400)/o).] (Round your answer to for decimal places.)
The shear strength of each of ten test spot welds is determined, yielding the following data (psi). 367 362 415 358 367 373 409 387 389 375 (a) Assuming that shear strength is normally distributed, estimate the true average shear strength and standard deviation of shear strength using the method of maximum likelihood. (Round your answers to two decimal places.) average standard deviation psi psi (b) Again assuming a normal distribution, estimate the strength value below which 95% of all welds will have their strengths. [Hint: What is the 95th percentile in terms of u and o? Now use the invariance principle.] (Round your answer to two decimal places.) psi (c) Suppose we decide to examine another test spot weld. Let X = shear strength of the weld. Use the given data to obtain the mle of P(X ≤ 400). [Hint: P(X ≤ 400) = ((400)/o).] (Round your answer to for decimal places.)
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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![### Shear Strength Analysis of Test Spot Welds
The shear strength of each of ten test spot welds is determined, yielding the following data (in psi):
```
367, 362, 415, 358, 367, 373, 409, 387, 389, 375
```
#### Problem (a)
Assuming that shear strength is normally distributed, estimate the true average shear strength and the standard deviation of shear strength using the method of maximum likelihood. (Round your answers to two decimal places.)
- **Average Shear Strength:**
```
[ ] psi
```
- **Standard Deviation of Shear Strength:**
```
[ ] psi
```
#### Problem (b)
Again assuming a normal distribution, estimate the strength value below which 95% of all welds will have their strengths.
*Hint:* What is the 95th percentile in terms of \(\mu\) and \(\sigma\)? Now use the invariance principle. (Round your answer to two decimal places.)
- **Strength Value (95th percentile):**
```
[ ] psi
```
#### Problem (c)
Suppose we decide to examine another test spot weld. Let \(X\) = shear strength of the weld. Use the given data to obtain the mile of \(P(X \leq 400)\). *Hint:* \(P(X \leq 400) = \Phi((400 - \mu)/\sigma)\) (Round your answer to four decimal places.)
- **P(X ≤ 400):**
```
[ ]
```
This analysis involves using statistical methods to derive essential characteristics of the shear strength of spot welds, which can help in ensuring the quality and reliability of welding processes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb989860-4d1c-4fb5-9e6b-42a4528dce9c%2F26a620ba-f34e-49c5-86a3-160915775aab%2Fqn8qnf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Shear Strength Analysis of Test Spot Welds
The shear strength of each of ten test spot welds is determined, yielding the following data (in psi):
```
367, 362, 415, 358, 367, 373, 409, 387, 389, 375
```
#### Problem (a)
Assuming that shear strength is normally distributed, estimate the true average shear strength and the standard deviation of shear strength using the method of maximum likelihood. (Round your answers to two decimal places.)
- **Average Shear Strength:**
```
[ ] psi
```
- **Standard Deviation of Shear Strength:**
```
[ ] psi
```
#### Problem (b)
Again assuming a normal distribution, estimate the strength value below which 95% of all welds will have their strengths.
*Hint:* What is the 95th percentile in terms of \(\mu\) and \(\sigma\)? Now use the invariance principle. (Round your answer to two decimal places.)
- **Strength Value (95th percentile):**
```
[ ] psi
```
#### Problem (c)
Suppose we decide to examine another test spot weld. Let \(X\) = shear strength of the weld. Use the given data to obtain the mile of \(P(X \leq 400)\). *Hint:* \(P(X \leq 400) = \Phi((400 - \mu)/\sigma)\) (Round your answer to four decimal places.)
- **P(X ≤ 400):**
```
[ ]
```
This analysis involves using statistical methods to derive essential characteristics of the shear strength of spot welds, which can help in ensuring the quality and reliability of welding processes.
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