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25 January, 12:53

After a million measurements of thing x, we find a sample mean of 30.49 and standard deviation of 1.95. What chance, in percent (0-100) does the next measurement have of being outside 1 standard deviation from the mean?

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  1. 25 January, 14:06
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    32%

    Step-by-step explanation:

    The Empirical Rule states that, for a normally distributed random variable:

    68% of the measures are within 1 standard deviation of the mean.

    95% of the measures are within 2 standard deviation of the mean.

    99.7% of the measures are within 3 standard deviations of the mean.

    The sampling distribution of the sample means tend to be normally distributed.

    What chance, in percent (0-100) does the next measurement have of being outside 1 standard deviation from the mean?

    68% of the measures are within 1 standard deviation of the mean.

    100 - 68 = 32% are outside of 1 standard deviation from the mean.

    So the chance is 32%.
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