# Standard Deviation & Probability of Error

A voltmeter is used to measure a known voltage of 100 V. Forty percent of the readings are within 0.5 V of the true value. Estimate the standard deviation for the meter. What is the probability of an error of 0.75 V?

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#### Solution Preview

You should have some source for calculating the integral probability of a normal distribution and its inverse.

I use the MatLab functions erf and erfinv.

The erf function is defined as

erf(x) = (2/sqrt(pi)) int_0^x e^{-t^2} dt,

so that the probability for a normally distributed quantity to deviate from its average by x times its standard deviation (x*SD) is

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$2.19