Suppose the time spent by a randomly selected student who uses a terminal connected to a local time-sharing computer facility has a gamma distribution with mean 20 min and variance 80 min2 . a) What are the values of α and ? b) What is the probability that a student uses the terminal for at most 24 min? c) What is the probability that a student spends between 20 and 40 min using the terminal?
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!
Suppose the time spent by a randomly selected student who uses a terminal connected to a
local time-sharing computer facility has a gamma distribution with
variance 80 min2
.
a) What are the values of α and ?
b) What is the
c) What is the probability that a student spends between 20 and 40 min using the
terminal?
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