Question 1205735: An electrician is testing the accuracy of resistors that have a nominal resistance of 15 S (ohms). She finds that the distribution of resistances is distributed normally with a mean of 15.08 S and a standard deviation of 1.52 2.
a. Is resistance an example of a discrete or continuous variable? Justify your answer.
Answer by math_tutor2020(3817)   (Show Source):
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Answer: continuous
Reason
We can pick any two positive distinct resistance values to compute the midpoint.
Examples:
The midpoint of 10 ohms and 12 ohms is 11 ohms.
The midpoint of 11 ohms and 12 ohms is 11.5 ohms.
The midpoint of 11.5 ohms and 12 ohms is 11.75 ohms.
Each midpoint is valid and possible. The process of computing the midpoint can be done indefinitely.
This is why the variable is continuous
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What's something that's discrete?
An example would be something like "The number of resistors to check".
It doesn't make sense to have 11.75 resistors since we can only have a nonnegative whole number of them (0,1,2,3,...).
Sometimes a midpoint is valid (say between 2 and 4) but other times a midpoint is not valid (eg: between 3 and 4)
If we focused on the discrete set {1,2,3,4} then it's clear that it's finite.
Meanwhile a continuous set of real numbers between 1 and 4 is infinite.
So this is another key distinction between discrete and continuous.
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