Final answer:
The interval estimate for the population mean μ, using a sample mean (x) of 27 and a margin of error of 5, is calculated as (22, 32). This means the true population mean is estimated to be between these two numbers.
Step-by-step explanation:
To construct an interval estimate for the population mean μ using the given sample mean (μ), which is x = 27, and a specified margin of error (EBM) of 5, we use the confidence interval (CI) formula. The CI is calculated as:
(point estimate - EBM, point estimate + EBM)
In this case, the point estimate is the sample mean (x), so the confidence interval would be:
(27 - 5, 27 + 5)
Therefore, the interval estimate for the population mean μ with a margin of error of 5 is (22, 32).
This interval means we are confident that the true population mean lies between 22 and 32. The choice of the confidence level (for example, 90%, 95%, etc.) would typically dictate the margin of error, but it is not specified in this example. Instead, we have used the given EBM to construct the estimate.