9) The time it takes a worker on an assembly line to complete a task is exponentially distributed with a mean of 8 minutes. a. What is the probability density function for the time it takes to complete the task? b. What is the probability that it will take a worker less than 4 minutes to complete the task? c. What is the probability that it will take a worker between 6 and 10 minutes to complete the task?
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!
9) The time it takes a worker on an assembly line to complete a task is exponentially distributed with a mean of 8 minutes.
a.
What is the
b.
What is the probability that it will take a worker less than 4 minutes to complete the task?
c.
What is the probability that it will take a worker between 6 and 10 minutes to complete the task?
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