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19 September, 23:33

Use the confidence level and Sample data to find a confidence interval for estimating the population mean. Round your answer to the same number of decimal places as the sample mean.

Of the packages received by a Parcel Service, 37 packages were randomly selected. The sample has a mean weight of 17.0 pounds and a standard deviation of 3.3 lb. What is the 95% confidence interval for the true mean weight, μ, of all packages received by the Parcel Service?

A) 15.7 lb<μ<18.3 lb

B) 15.9 lb<μ<18.1 lb

C) 15.6 lb<μ<18.4 lb

D) 16.1 lb<μ<17.9 lb

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  1. 19 September, 23:37
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    B) 15.9 lb < μ < 18.1 lb

    Step-by-step explanation:

    Confidence interval = mean ± margin of error

    CI = μ ± ME

    The mean is μ = 17.0.

    Margin of error = critical value * standard error

    ME = CV * SE

    n > 30, so we can approximate CV with a normal distribution. At P = 95%, CV = 1.96.

    SE = σ / √n

    SE = 3.3 / √37

    SE = 0.54

    So the margin of error is:

    ME = 1.96 * 0.54

    ME = 1.1

    So the confidence interval is:

    CI = 17.0 ± 1.1

    CI = (15.9, 18.1)
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