Each sweat shop worker at a computer factory can put together 4 computers per hour on average with a standard deviation of 1 computers. 42 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. If one randomly selected worker is observed, find the probability that this worker will put together between 3.8 and 4 computers per hour.  For the 42 workers, find the probability that their average number of computers put together per hour is between 3.8 and 4.  Find the probability that a 42 person shift will put together between 163.8 and 168 computers per hour.

Each sweat shop worker at a computer factory can put together 4 computers per hour on average with a standard deviation of 1 computers. 42 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.

  1. If one randomly selected worker is observed, find the probability that this worker will put together between 3.8 and 4 computers per hour. 
  2. For the 42 workers, find the probability that their average number of computers put together per hour is between 3.8 and 4. 
  3. Find the probability that a 42 person shift will put together between 163.8 and 168 computers per hour. 
  4. A sticker that says “Great Dedication” will be given to the groups of 42 workers who have the top 20% productivity. What is the least total number of computers produced by a group that receives a sticker? minutes (round to the nearest computer)
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