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This problem says a computer technician believes the upload speed offered by a new internet company in town is not as fast as advertised.
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Assume the upload speed follows an unknown distribution with a mean of 38 mpps and a standard deviation of 11.
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And if the technician randomly selects 32 internet connections, use the graph below to calculate the probability that the sample mean is between 32 and 34.
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And we're asked to use the central limit theorem to find the mean of the sampling distribution and the standard deviation of the sample mean.
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And here, because our n value is greater than equal to 30, that means the central limit theorem does apply.
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And that means that the mean of our sampling distribution will be equivalent to the mean of the population, so that would stay 38.
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And the standard deviation of the sampling distribution of the sample mean is equal to the standard deviation of the population divided by the square to the sample size n.
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So in our case, that will be 11 divided by the square to 32.
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And rounded to two decimal places, that gives us the result for the standard deviation.
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Of 1 .94...