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.