Question

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 = 3.12 mA with standard deviation σ = 1.17 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

Answer 1

In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68%, 95% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively.

a. So for 68% answer is &

So answer is

from 1.95 mA to 4.29 mA

b. For 95%, &

So answer is

from 0.78 mA to 5.46 mA