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

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To calculate the standard deviation of a voltmeter measuring 100V, it is essential to recognize that 40% of the readings fall within ±0.5V of the true value, indicating a confidence interval (CI) of 100V ± 0.5V. The readings are likely normally distributed, which allows for the use of Z-scores to determine the standard deviation. The sample size (n) is not 40; instead, it refers to the percentage of readings that meet the criteria. To find the mean, one should average the values within the specified range, but the exact method requires clarification on the total number of readings. Understanding these concepts will help in calculating both the standard deviation and the probability of an error of 0.75V.
OEstudent
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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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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.
 
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