Question

Each sweat shop worker at a computer factory can put together 4.5 computers per hour on average with a standard deviation of 0.8 computers. 8 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. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
4. If one randomly selected worker is observed, find the probability that this worker will put together between 4.6 and 4.7 computers per hour.
5. For the 8 workers, find the probability that their average number of computers put together per hour is between 4.6 and 4.7.
6. Find the probability that a 8 person shift will put together between 33.6 and 36.8 computers per hour.
7. For part e) and f), is the assumption of normal necessary? YesNo
8. A sticker that says "Great Dedication" will be given to the groups of 8 workers who have the top 15% productivity. What is the least total number of computers produced by a group that receives a sticker? minutes (round to the nearest computer)

Answer 1