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19 February, 12:47

A statistics practitioner determined that the mean and standard deviation of a data set were 120 and 30, is respectively. What can you say about the proportions of observations that lie between each of the follow - ing intervals?

a. 90 and 150

b. 60 and 180

c. 30 and 210

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  1. 19 February, 13:08
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    a) 68% of the observations lie between 90 and 150.

    b) 95% of the observations lie between 60 and 180.

    c) 99.7% of the observations lie between 30 and 210.

    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.

    In this problem, we have that:

    Standard deviation = 120

    Mean = 30

    a. 90 and 150

    This is within 1 standard deviation of the mean.

    By the Empirical Rule, 68% of the observations lie between 90 and 150.

    b. 60 and 180

    This is within 2 standard deviations of the mean.

    By the Empirical Rule, 95% of the observations lie between 60 and 180.

    c. 30 and 210

    This is within 3 standard deviations of the mean.

    By the Empirical Rule, 99.7% of the observations lie between 30 and 210.
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