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?**\[ ??? \text{ computers per hour (round to the nearest computer)} \]

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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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