a) What is the standard deviation of the time spent with a patient? b) What is the likelihood that the physician will spend less than 35 minutes with a patient? c) A patient has an appointment to see the physician at 8AM on a particular day. When should the second patient be scheduled so that there is only a 15% chance s/he will have to wait before before being seen by the physician? [e.g. if the appointment for the second patient is 8:15AM, there is a 100% chance the second patient will have to wait]
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!
A physician sees many different kinds of patients, and thus the time spent with each patient varies. Let X be the time spent with a patient in minutes. From historical data, X is known to be uniformly distributed between 15 and 40 minutes.
a) What is the standard deviation of the time spent with a patient?
b) What is the likelihood that the physician will spend less than 35 minutes with a patient?
c) A patient has an appointment to see the physician at 8AM on a particular day. When should the second patient be scheduled so that there is only a 15% chance s/he will have to wait before before being seen by the physician? [e.g. if the appointment for the second patient is 8:15AM, there is a 100% chance the second patient will have to wait]
The standard deviation of the time spent with a patient can be calculated as:
Thus, the standard deviation is 7.217
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