Each sweat shop worker at a computer factory can put together 4 computers per hour on average with a standard deviation of 0.8 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 3.9 and 4 computers per hour. For the 42 workers, find the probability that their average number of computers put together per hour is between 3.9 and 4. Find the probability that a 42 person shift will put together between 163.8 and 168 computers per hour
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Each sweat shop worker at a computer factory can put together 4 computers per hour on average with a standard deviation of 0.8 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
- If one randomly selected worker is observed, find the
probability that this worker will put together between 3.9 and 4 computers per hour. - For the 42 workers, find the probability that their average number of computers put together per hour is between 3.9 and 4.
- Find the probability that a 42 person shift will put together between 163.8 and 168 computers per hour.
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