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10 June, 08:27

A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. the reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. suppose the reported values are the true mean and standard deviation for the population of subjects in the study. if a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 seconds?

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  1. 10 June, 09:47
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    It can be considered that the distribution of the sample is normal, based on the central limit theorem, where the sigma of the sample is:σ / root (n).

    The mean of the sample is:

    μm = μ

    So:

    P (X> 11) = P (Z> Zo).

    Where Z follows a standard normal distribution and

    Zo = (μm-μ) / (σ / root (n))

    Zo = (11-10.2) / (16 / root (144)).

    Zo = 0.6

    From the table for the standard normal distribution we have to:

    P (Z> 0.6) = 0.2743
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