A student takes the campus shuttle bus to reach the classroom building. The shuttle bus arrives at his stop every 15 minutes but the actual arrival time at the stop is random. The student allows 10 minutes waiting time for the shuttle in his plan to make it in time to the class. What is the expected waiting time? What is the variance? What is the probability that the wait will be between four and six minutes? What is the probability that the student will be in time for the class? If he wants to be 95% confifident of being on time for the class, how much time should he allow for waiting for the shuttle?
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!
3–50. A student takes the campus shuttle bus to reach the classroom building. The
shuttle bus arrives at his stop every 15 minutes but the actual arrival time at the stop
is random. The student allows 10 minutes waiting time for the shuttle in his plan to
make it in time to the class.
- What is the expected waiting time? What is the variance?
- What is the probability that the wait will be between four and six minutes?
- What is the probability that the student will be in time for the class?
- If he wants to be 95% confifident of being on time for the class, how much
time should he allow for waiting for the shuttle?
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