How Do You Calculate Standard Deviation and Error Probability for a Voltmeter?

You can use the formula (Zα∗ σ)/√n for the standard deviation and substitute the values for n (40), Zα (1.28 for 40% CI), and the known voltage of 100V. This will give you the standard deviation of the voltmeter, which is the measure of precision. To find the probability of an error of 0.75V, you can use the normal distribution table to find the area under the curve for a range of ±0.375V (half of the 0.75V). This will give you the probability of an error within that range. In summary, you can use the formula (Zα∗ σ)/√n to find the
  • #1
OEstudent
1
0
1. A voltmeter is used to measure a known voltage of 100V. Forty percent of the readings are within 0.5V of true value. How do I figure out the standard deviation of the voltmeter, and how do I figure out the probability of an error of 0.75V?



2. I am trying to figure this problem out, however I do not know what to do with the 40% of the readings. Is that my n? Is n=40? And is the mean (99.5+99.6+99.7+99.8+99.9+100+100.1+100.2+100.3+100.4+100.5)/40? I am doing circles trying to figure this out.



Thanks for any input and help, OEstudent
 
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  • #2
You have a 40% CI of 100V ± 0.5 V

Most likely your readings are normally distributed. So you need to get the Zα value and use the formula for the CI.
 

Related to How Do You Calculate Standard Deviation and Error Probability for a Voltmeter?

1. What is standard deviation?

Standard deviation is a measure of how spread out a set of data is from its mean or average. It shows the amount of variation or dispersion within the data set.

2. Why is standard deviation important?

Standard deviation is important because it provides a way to understand the variation or diversity of a data set. It helps to identify outliers and measure the precision of data. It is also used in many statistical calculations and can give insights into the reliability of data.

3. How is standard deviation calculated?

Standard deviation is calculated by taking the square root of the variance. The variance is found by subtracting each data point from the mean, squaring the differences, and then finding the average of those squared differences.

4. How is standard deviation interpreted?

The standard deviation is typically interpreted in relation to the mean of the data set. A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation means that the data points are more spread out from the mean. It can also be used to compare the variation between different data sets.

5. Can standard deviation be negative?

No, standard deviation cannot be negative. It is a measure of distance from the mean, so it will always be a positive value. If a calculation results in a negative value, it means there was an error in the calculation.

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