At an urgent care facility, patients arrive at an average rate of one patient every seven minutes. Assume that the duration between arrivals is exponentially distributed. a. Find the probability that the time between two successive visits to the urgent care facility is less than 2 minutes. b. Find the probability that the time between two successive visits to the urgent care facility is more than 50 minutes. c. If 10 minutes have passed since the last arrival, what is the probability that the next person will arrive within the next 5 minutes? d. Find the probability that more than eight patients arrive during a half hour period.
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!
At an urgent care facility, patients arrive at an average rate of one patient every seven minutes. Assume that the duration between arrivals is exponentially distributed.
a. Find the probability that the time between two successive visits to the urgent care facility is less than 2 minutes.
b. Find the probability that the time between two successive visits to the urgent care facility is more than 50 minutes.
c. If 10 minutes have passed since the last arrival, what is the probability that the next person will arrive within the next 5 minutes?
d. Find the probability that more than eight patients arrive during a half hour period.
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