EmergencyRoomTraffic. Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a special type of reverse-J-shaped distribution called an exponential distribution. They also indicate that the mean time between arriving patients is 8.7 minutes, as is the standard deviation. Suppose that you observe a sample of 10 interarrival times. a. Theoretically, what are the mean and standard deviation of all possible sample means? b. Use the technology of your choice to simulate 1000 samples of 10 interarrival times each. c. Determine the mean of each of the 1000 samples you obtained in part (b). d. Roughly what would you expect the mean and standard deviation of the 1000 sample means you obtained in part (c) to be? Explain your answers. e. Determine the mean and standard deviation of the 1000 sample means you obtained in part (c). f. Compare your answers in parts (d) and (e). Why are they different?
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!
EmergencyRoomTraffic. Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a special type of reverse-J-shaped distribution called an exponential distribution. They also indicate that the mean time between arriving patients is 8.7 minutes, as is the standard deviation. Suppose that you observe a sample of 10 interarrival times.
a. Theoretically, what are the mean and standard deviation of all possible sample means?
b. Use the technology of your choice to simulate 1000 samples of 10 interarrival times each.
c. Determine the mean of each of the 1000 samples you obtained in part (b).
d. Roughly what would you expect the mean and standard deviation of the 1000 sample means you obtained in part (c) to be? Explain your answers.
e. Determine the mean and standard deviation of the 1000 sample means you obtained in part (c).
f. Compare your answers in parts (d) and (e). Why are they different?
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