# Probability from the tolerance of a capacitor (Gaussian distribution)

• Peter Alexander
In summary, the text asks for the probability that a capacitance is greater than 30nF. To find this, you would need to find the area under the normal distribution curve from 30nF to infinity, which is 0.5.
Peter Alexander
Homework Statement
Given a capacitor with 33 nF
Task requires you to compute the probability for a capacitance being greater than 30nF, given that there's 20% tolerance (3σ).
Relevant Equations
The formula for Gaussian distribution (https://en.wikipedia.org/wiki/Normal_distribution)
Given the upper data, if the nominal value for capacitance is 33nF and tolerance of 20%, then values can range between 26.4nF and 39.6nF. With the bottom margin being set at 30nF, this means that the interval takes approximately 72% of all values.

Is this the correct procedure to solve this task?

Any sort of help would be appreciated.

No. How did you determine the 0.72 ?

BvU said:
No. How did you determine the 0.72 ?

By dividing the interval 30 - 39.6 from 26.4 - 39.6.

If you find the z-value associated with 30, meaning the number of ##\sigma## from the expected value, you can just look up the associated percent/percentile in a standard normal table. Edit: I am assuming from your post that the data in question are normally-distributed. Please let me know if that is not correct or must be proven first.

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Peter Alexander said:
By dividing the interval 30 - 39.6 from 26.4 - 39.6.
It would be clearer if you posted something like ' I did (39.6-30)/(39.6-26.4) = 0.727 '

Which is definitely not the idea of this exercise.

Another notion that needs correction is
Peter Alexander said:
values can range between 26.4nF and 39.6nF
because the exercise text clearly implies that the capacitance is distributed according to a normal distribution with average 33 nF and a standard deviation of 6.6/3 nF = 2.2 nF.
That means capacitances can range between ##-\infty## and ##+\infty##
(not to worry, the probabilities decrease very rapidly outside reasonable ranges. But theoretically they are not zero !)
Just a consequence of the assumed probability distribution model -- for which very good but not perfect arguments exist.

In fact, outside the range average ##\pm 3\sigma##, 0.27% of the values are theoretically expected.

Now, what are you supposed to do: given the average value of 33 nF and the standard deviation of 2.2 nF
compute the probability for a capacitance being greater than 30nF

Suppose you have a standard normal distribution plot in front of you ,

the probability to find any value corresponds to the total area under the curve: 1 (or also expressed as 100%)
the probability to find a value > 33nF corresponds to the area under the curve from 33 nF to infinity: 0.5 (from symmetry)

Can you describe what area corresponds to the probablity the exercise asks for ?------------------------------------

Another important bit of wise-guy comment:
What we casually call probablility distributions are actually plots of probability densities . Probabilities emerge when we multiply with a range: probability for a value to be in ##[x, x+dx]## is equal to ##P(x)\, dx##.​

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## 1. What is probability in relation to the tolerance of a capacitor?

Probability is a measure of the likelihood that a certain event will occur. In the context of the tolerance of a capacitor, probability is used to determine the chances of a capacitor falling within a certain range of values.

## 2. How is probability calculated for the tolerance of a capacitor?

The probability of a capacitor falling within a certain tolerance range can be calculated using the Gaussian distribution, also known as the normal distribution. This calculation takes into account the mean value and standard deviation of the tolerance range.

## 3. What is the significance of a Gaussian distribution in relation to capacitor tolerance?

The Gaussian distribution is a bell-shaped curve that is commonly seen in natural phenomena. It is used in the context of capacitor tolerance because it accurately represents the distribution of values within a tolerance range, with most values falling close to the mean value and fewer values falling farther away from the mean.

## 4. How does capacitor tolerance affect the probability of a malfunction?

The tolerance of a capacitor can greatly affect the probability of a malfunction occurring. A wider tolerance range means a higher chance of the capacitor falling outside of the desired range, which can lead to a malfunction in the circuit or device it is used in.

## 5. Are there any factors that can affect the probability of a capacitor's tolerance?

Yes, there are several factors that can affect the probability of a capacitor's tolerance. These include manufacturing processes, environmental factors, and the quality of materials used in the capacitor. These factors can all contribute to variations in the tolerance range and therefore affect the probability of a capacitor functioning within the desired range.

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