Each minute a machine produces a length of rope with mean 4 feet and standarddeviation 0.5 feet. Assume that the amounts produced in different minutes are independent andidentically distributed. (a) Assume the amount produced in each minute has a normal distribution. Find the probability that the machine will produce at least 250 feet in one hour. (b) How would your answer in (a) change if the distribution of the amount produced in each minute is not normally distributed?
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 minute a machine produces a length of rope with mean 4 feet and standarddeviation 0.5 feet. Assume that the amounts produced in different minutes are independent andidentically distributed.
(a) Assume the amount produced in each minute has a normal distribution. Find the probability that the machine will produce at least 250 feet in one hour.
(b) How would your answer in (a) change if the distribution of the amount produced in each minute is not
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