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    Question about Compute the probability

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    A population of unknown shape has a mean of 75. You select a sample of 40. The standard deviation of the sample is 5. Compute the probability the sample mean is:
    a. Less than 74.
    b. Between 74 and 76.
    c. Between 76 and 77.
    d. Greater than 77.

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    Solution Preview

    Assuming that Central Limit Theorem holds,and use the z distribution tables for calculations:

    For this problem the STD of the sample mean is 5/sqrt(40) = 0.7906 .
    So we have a normal distributed ramdom variable X with mean Mu = 75
    and standard deviation StD = 0.7906

    -Compute the probability the sample ...

    Solution Summary

    This solution explains how the central limit theorem is used to estimate the mean of a sample based on information about the population.