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To estimate the mean weight of the packages with a 95% confidence interval of +/-1.5 pounds, you need to determine the sample size (number of randomly selected packages).
The formula to determine the required sample size is:
n = (Z * σ / E)^2
where:
n = sample size
Z = Z-score for desired confidence level (95% confidence level corresponds to a Z-score of approximately 1.96)
σ = standard deviation of all weights
E = desired margin of error (+/-1.5 pounds in this case)
In this case, the standard deviation (σ) is given as around 8 pounds.
Plugging the values into the formula:
n = (1.96 * 8 / 1.5)^2
n ≈ 10.389^2
n ≈ 107.82
So, you would need to randomly select approximately 108 packages to estimate the mean weight with a 95% confidence interval of +/-1.5 pounds, based on prior studies indicating a standard deviation of 8 pounds.