The time that it takes for the next train to come follows a Uniform distribution with f(x) =1/50 where x goes between 2 and 52 minutes. Round answers to 4 decimal places when possible. E. Find the probability that the time will be at most 15 minutes. F. Find the probability that the time will be between 17 and 29 minutes. G. Find the 18th percentile.
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!
The time that it takes for the next train to come follows a Uniform distribution with f(x) =1/50 where x goes between 2 and 52 minutes. Round answers to 4 decimal places when possible.
E. Find the
F. Find the probability that the time will be between 17 and 29 minutes.
G. Find the 18th percentile.
H. Find the probability that the time is more than 19 minutes given (or knowing that) it is at least 17 minutes.
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