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29 May, 04:32

a sample of 144 was taken from a population with a standard deviation of 36 inches. In this case the sample mean will be within how many inches of the population mean 99.7% of thew time?

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  1. 29 May, 06:01
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    9 inches

    Step-by-step explanation:

    The population is within 6 standard deviations of the mean with a confidence of 99.7 percent, 3 above and 3 below

    The standard deviation of the sample mean is equal to the population standard deviation divided by the square root of the sample size

    population standard deviation = 36

    sample size = 144

    standard deviation of the sample mean = 36 / sqrt (144)

    =36/12

    =3

    The margin of error is the number of standard deviations above the mean * the standard deviations

    margin of error = 3 * 3

    = 9 inches
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