In a certain article, laser therapy was discussed as a useful alternative to drugs in pain management of chronically ill patients. To measure pain threshold, a machine was used that delivered low-voltage direct current to different parts of the body (wrist, neck, and back). The machine measured current in milliamperes (mA). The pretreatment experimental group in the study had an average threshold of pain (pain was first detectable) at μ = 3.11 mA with standard deviation σ = 1.16 mA. Assume that the distribution of threshold pain, measured in milliamperes, is symmetric and more or less mound-shaped. (Round your answers to two decimal places.) (a) Use the empirical rule to estimate a range of milliamperes centered about the mean in which about 68% of the experimental group will have a threshold of pain from __________ mA to ___________ mA (b) Use the empirical rule to estimate a range of milliamperes centered about the mean in which about 95% of the experimental group will have a threshold of pain from __________ mA to _________ mA
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!
In a certain article, laser therapy was discussed as a useful alternative to drugs in pain management of chronically ill patients. To measure pain threshold, a machine was used that delivered low-voltage direct current to different parts of the body (wrist, neck, and back). The machine measured current in milliamperes (mA). The pretreatment experimental group in the study had an average threshold of pain (pain was first detectable) at μ = 3.11 mA with standard deviation σ = 1.16 mA. Assume that the distribution of threshold pain, measured in milliamperes, is symmetric and more or less mound-shaped. (Round your answers to two decimal places.)
(a) Use the
from __________ mA to ___________ mA
(b) Use the empirical rule to estimate a range of milliamperes centered about the mean in which about 95% of the experimental group will have a threshold of pain
from __________ mA to _________ mA
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