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 08 b. What is the distribution of ? - N 4.6 0.225 ✓ or or c. What is the distribution of Σx? Σx - N( 73.6 3.6 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. 0.1309 X 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. 0.4833 X f. Find the probability that a 16 person shift will put together between 72 and 75.2 computers per hour. 0.3400 X g. For part e) and f), is the assumption of normal
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 08 b. What is the distribution of ? - N 4.6 0.225 ✓ or or c. What is the distribution of Σx? Σx - N( 73.6 3.6 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. 0.1309 X 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. 0.4833 X f. Find the probability that a 16 person shift will put together between 72 and 75.2 computers per hour. 0.3400 X g. For part e) and f), is the assumption of normal
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
Help with red and blank ones please

Transcribed Image Text:### Statistical Analysis of Computer Assembly Workers' Productivity
Each worker at a computer factory can assemble an average of 4.6 computers per hour, with a standard deviation of 0.9 computers per hour. A group of 16 workers is randomly selected to work the next shift. This analysis uses a normal distribution to answer each question and rounds answers to four decimal places where possible.
#### a. Distribution of Individual Worker Productivity
**Question:** What is the distribution of \( X \)?
**Answer:** \( X \sim \mathcal{N}(4.6, 0.9) \)
#### b. Distribution of Average Productivity for 16 Workers
**Question:** What is the distribution of \( \bar{x} \)?
**Answer:** \( \bar{x} \sim \mathcal{N}(4.6, 0.225) \)
#### c. Distribution of Total Productivity for 16 Workers
**Question:** What is the distribution of \( \sum x \)?
**Answer:** \( \sum x \sim \mathcal{N}(73.6, 3.6) \)
#### d. Probability for One Worker to Assemble Between 4.4 and 4.7 Computers
**Question:** If one randomly selected worker is observed, find the probability that this worker will assemble between 4.4 and 4.7 computers per hour.
**Answer:** 0.1309 (Incorrect as per the validation marks in the image)
#### e. Probability for 16 Workers' Average Productivity to be Between 4.4 and 4.7 Computers
**Question:** For the 16 workers, find the probability that their average number of computers assembled per hour is between 4.4 and 4.7.
**Answer:** 0.4833 (Incorrect as per the validation marks in the image)
#### f. Probability for 16 Workers' Total Productivity to be Between 72 and 75.2 Computers
**Question:** Find the probability that a 16-person shift will assemble between 72 and 75.2 computers per hour.
**Answer:** 0.3400 (Incorrect as per the validation marks in the image)
#### g. Assumption of Normal Distribution
**Question:** For parts e) and f), is the assumption of normal distribution necessary?
**Answer:** Yes
#### h. Productivity Threshold for Top 20% Performance
**Question:** A sticker that says "Great Ded
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 4 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