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I have a value x = 60 ± 5.5, and I want to find the population mean μ_x (mean of x), and the population variance of x. How can I do do this?

Sorry for the noob question, but I've spent 3 hours trying to get a concrete answer for this. I can elaborate if any detail is missing/needed for answering this question.

Thank you very much.

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  • $\begingroup$ Something is missing. Consider this: If you know $P(54.5 < X < 65.6) = 0.95$ Then for a normal distribution, $1.96\sigma = 5.5,$ making $\sigma = 2.80.$ In R, where pnorm is a normal CDF, code diff(pnorm(c(54.5,65.5), 60, 2.8)) returns $0.950503.$ $\endgroup$
    – BruceET
    Mar 6, 2021 at 1:04

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Nevermind, I found an answer. μ_x = 60, and variance = 5.5.

Source: solution for the question in which I needed to find these.

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    $\begingroup$ Your solution either gives the wrong answer, badly abuses terminology, or is quoted out of context. I recommend discussing this question further. $\endgroup$
    – Dave
    Mar 5, 2021 at 23:41
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    $\begingroup$ In $60 \pm 5.5$ the $5.5$ is unlikely to be the variance $\endgroup$
    – Henry
    Mar 6, 2021 at 0:02
  • $\begingroup$ Perhaps more likely, 5.5 is about twice $\sigma.$ $\endgroup$
    – BruceET
    Mar 6, 2021 at 1:07

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