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19 September, 08:26

A population has a standard deviation of 25 and a mean of 300. Given a random sample of size 100, how likely is it that the sample mean will be within / - 5 of the population mean?

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  1. 19 September, 08:35
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    95%

    Step-by-step explanation:

    Margin of error is the standard error times critical value.

    ME = SE * CV

    The standard error for a sample mean is:

    SE = σ / √n

    SE = 25 / √100

    SE = 2.5

    If the margin of error is ±5, then the critical value is:

    5 = 2.5 CV

    CV = 2

    Since the sample size is greater than 30, we can approximate the confidence level using normal distribution. The percent between - 2 and 2 standard deviations is 95%.

    Therefore, there is a 95% probability the sample mean is within ±5 of the population mean.
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