A bus comes by every 12 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 12 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the person will wait more than 9 minutes is d. Suppose that the person has already been waiting for 0.3 minutes. Find the probability that the person's total waiting time will be between 0.9 and 1.5 minutes e. 92% of all customers wait at least how long for the train? minutes.
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!
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