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 = 3.02 mA with standard deviation σ = 1.21 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

Solution :

Given that,

= 3.02

= 1.21

Using Empirical rule,

(a)

P( - 1< X < + 1) = 68%

P(3.02 - 1.21 < X < 3.02 + 1.21) = 68%

P(1.81 < X < 4.23) = 68%

About 68% of the experimental group will have a threshold of pain from 1.81 mA to 4.23 mA

(b)

P( - 2< X < + 2) = 95%

P(3.02 - 2 * 1.21 < X < 3.02 + 2 * 1.21) = 95%

P(0.6 < X < 5.44) = 95%

About 95% of the experimental group will have a threshold of pain from  0.6 mA to 5.44 mA