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how large a sample should be selected to provide a confidence interval with a margin of error of 2 ? assume that the population standard deviation is 40. round your answer to next whole number.

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Final answer:

To provide a confidence interval with a margin of error of 2, given a population standard deviation of 40 and using a typical 95% confidence level, you need a sample size of 385.

Step-by-step explanation:

To determine how large a sample should be selected to provide a confidence interval with a margin of error of 2, we can use the formula for the sample size for estimating a population mean:

n = (Z*σ/E)^2,

where n is the sample size, Z is the Z-score corresponding to the desired confidence level, σ is the population standard deviation, and E is the margin of error. Assuming a 95% confidence level (which is typical in such calculations), we use a Z-score of approximately 1.96. Given the population standard deviation (σ) of 40 and a margin of error (E) of 2:

n = (1.96 * 40/2)^2 = 384.16,

which rounds up to the next whole number, giving us a sample size of 385.

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