Emergency Room Traffic. Desert Samaritan Hospital in Mesa, Arizona, keeps records of its emergency-room traffic. Beginning at 6:00 P.M. on any given day, the elapsed time, in hours, until the first patient arrives is a variable with density curve y = 6.9e−6.9x for x >0, and y = 0 otherwise. Here e is Euler’s number, which is approximately 2.71828. Most calculators have an e-key. Using calculus, it can be shown that the area under this density curve to the left of any number x greater than 0 equals 1 − e−6.9x. a. Graph the density curve of this variable. b. What percentage of the time does the first patient arrive between 6:15 P.M. and 6:30 P.M.?
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!
Emergency Room Traffic. Desert Samaritan Hospital in Mesa, Arizona, keeps records of its emergency-room traffic. Beginning at 6:00 P.M. on any given day, the elapsed time, in hours, until the first patient arrives is a variable with density curve y = 6.9e−6.9x for x >0, and y = 0 otherwise. Here e is Euler’s number, which is approximately 2.71828. Most calculators have an e-key. Using calculus, it can be shown that the area under this density curve to the left of any number x greater than 0 equals 1 − e−6.9x.
a. Graph the density curve of this variable.
b. What percentage of the time does the first patient arrive between 6:15 P.M. and 6:30 P.M.?
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