Given an sample of data set X which is normal-distributed to&nbsp;N(μ=240,σ), I want to find the&nbsp;95%&nbsp;confidence interval of&nbsp;max(μ−200,0). As the&nbsp;max(μ−200,0)&nbsp;cut the normal-distribution curve at the point of 200, the sample of&nbsp;max(μ−200,0)&nbsp;is not more normal distributed. Therefore what is a reasonable&nbsp;95%&nbsp;confidence interval?

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Given an sample of data set X which is normal-distributed to&amp;nbsp;N(μ=240,σ), I want to find the&amp;nbsp;95%&amp;nbsp;confidence interval of&amp;nbsp;max(μ−200,0). As the&amp;nbsp;max(μ−200,0)&amp;nbsp;cut the normal-distribution curve at the point of 200, the sample of&amp;nbsp;max(μ−200,0)&amp;nbsp;is not more normal distributed. Therefore what is a reasonable&amp;nbsp;95%&amp;nbsp;confidence interval?

Drahthaare89c · Accepted Answer

Step 1Your distribution contains a δ-function at x=0 of probability mass equal to the probability mass of your normal distribution less than the value x=200. (This will involve an error function.) The remaining probability mass will be due to the portion of your Gaussian to the right of x=200. As such, your 95% confidence interval will extend from x=0 up to the value x for which 5% of the total probability mass (or 10% of the truncated Gaussian) is above x. Clearly, this is expressed as an error function.

Given an sample of data set X which

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