The number of minutes that a patient waits at a medical clinic to see a doctor is represented by a uniform distribution between zero and 30 minutes, inclusive. (a) If X equals the number of minutes a person waits, what is the distribution of X? (b) Write the probability density function for this distribution. (c) What is the mean and standard deviation for waiting time? (d) What is the probability that a patient waits less than ten 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!
The number of minutes that a patient waits at a medical clinic to see a doctor is represented by a uniform distribution between zero and 30 minutes, inclusive.
(a) If X equals the number of minutes a person waits, what is the distribution of X?
(b) Write the
(c) What is the mean and standard deviation for waiting time?
(d) What is the probability that a patient waits less than ten minutes?
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