Each sweat shop worker at a computer factory can put together 4.6 computers per hour on average with a standard deviation of 0.9 computers. 16 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N 4.6 0.9 b. What is the distribution of ? - N 4.6 0.225 ✔ 0° c. What is the distribution of Σx? Σ - N( X 73.6 4 X 073.6 d. If one randomly selected worker is observed, find the probability that this worker will put together between 4.4 and 4.7 computers per hour. 0.11791 X e. For the 16 workers, find the probability that their average number of computers put together
Each sweat shop worker at a computer factory can put together 4.6 computers per hour on average with a standard deviation of 0.9 computers. 16 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N 4.6 0.9 b. What is the distribution of ? - N 4.6 0.225 ✔ 0° c. What is the distribution of Σx? Σ - N( X 73.6 4 X 073.6 d. If one randomly selected worker is observed, find the probability that this worker will put together between 4.4 and 4.7 computers per hour. 0.11791 X e. For the 16 workers, find the probability that their average number of computers put together
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Each sweatshop worker at a computer factory can put together 4.6 computers per hour on average with a standard deviation of 0.9 computers. 16 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution.
**a. What is the distribution of \( X \)?**
\[ X \sim N(4.6, 0.9) \]
**b. What is the distribution of \( \overline{X} \)?**
\[ \overline{X} \sim N(4.6, 0.225) \]
**c. What is the distribution of \( \sum X \)?**
\[ \sum X \sim N(73.6, ???) \]
**d. If one randomly selected worker is observed, find the probability that this worker will put together between 4.4 and 4.7 computers per hour.**
\[ ??? \]
**e. For the 16 workers, find the probability that their average number of computers put together per hour is between 4.4 and 4.7.**
\[ ??? \]
**f. Find the probability that a 16-person shift will put together between 72 and 75.2 computers per hour.**
\[ ??? \]
**g. For part e) and f), is the assumption of normal necessary?**
\[ \circ \text{Yes} \quad \circ \text{No} \]
**h. A sticker that says "Great Dedication" will be given to the groups of 16 workers who have the top 20% productivity. What is the least total number of computers produced by a group that receives a sticker?**
\[ ??? \text{ computers per hour (round to the nearest computer)} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb954a688-5e54-4f96-9877-503883322f61%2F6bb57048-40a3-42a2-9266-4b18299db3ef%2Fgtvjlc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Each sweatshop worker at a computer factory can put together 4.6 computers per hour on average with a standard deviation of 0.9 computers. 16 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution.
**a. What is the distribution of \( X \)?**
\[ X \sim N(4.6, 0.9) \]
**b. What is the distribution of \( \overline{X} \)?**
\[ \overline{X} \sim N(4.6, 0.225) \]
**c. What is the distribution of \( \sum X \)?**
\[ \sum X \sim N(73.6, ???) \]
**d. If one randomly selected worker is observed, find the probability that this worker will put together between 4.4 and 4.7 computers per hour.**
\[ ??? \]
**e. For the 16 workers, find the probability that their average number of computers put together per hour is between 4.4 and 4.7.**
\[ ??? \]
**f. Find the probability that a 16-person shift will put together between 72 and 75.2 computers per hour.**
\[ ??? \]
**g. For part e) and f), is the assumption of normal necessary?**
\[ \circ \text{Yes} \quad \circ \text{No} \]
**h. A sticker that says "Great Dedication" will be given to the groups of 16 workers who have the top 20% productivity. What is the least total number of computers produced by a group that receives a sticker?**
\[ ??? \text{ computers per hour (round to the nearest computer)} \]
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 5 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman