What is the confidence interval for a 100 ohm resistor with 10% tolerance?

[vptran84]

What is the 95% confidence interval for 100 ohm resister with 10% tolerence?

Here is my work so far, can someone please tell me if I am doing it wrong or right? Thank you in advance.

from table 95%: k = 1.96
100 * 0.1( which is the 10% tolerance) = 10

10 / sigma >= 1.96
Sigma <= 5.10204

confidence interval limits:
100ohm +- 1.96(5.10204ohms) = 100ohm +- 10ohms

 

[juvenal]

Maybe my definition of tolerance is wrong, but isn't 1 sigma = 10% * 100ohms = 10 ohms?

A 95% confidence interval would then be +/- 1.96 sigma.

 

[tacman]

Your work looks correct so far. To find the 95% confidence interval, we can use the formula:

95% CI = mean +/- margin of error

The mean in this case is 100 ohms, and the margin of error is 10 ohms (calculated from the tolerance of 10%). Therefore, the 95% confidence interval for a 100 ohm resistor with 10% tolerance would be:

95% CI = 100 ohms +/- 10 ohms

This means that we can be 95% confident that the true resistance of the resistor falls within the range of 90 ohms to 110 ohms.