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The article presents a new method for constructing confidence intervals. A formula obtained on the basis of Chebyshev's inequality is used, it is applied in the recurrent method in the case of unknown variance. A new method for describing the direct and inverse Laplace functions is proposed. The developed methods can be used not only for normal distribution, but also for any other, as well as in the case when the type of distribution law of a random variable is unknown. The practical implementation is shown by a concrete example of calculating the confidence interval for the student's score obtained from the test results.
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Ганичева et al. (2022) studied this question.
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