Final answer:
The question involves constructing a confidence interval for a population mean using a known population variance and the sample mean. The Central Limit Theorem and Z-distribution are employed in this statistical process.
Step-by-step explanation:
The question pertains to the field of statistics, specifically to the construction of a confidence interval for a population mean (μ) when the population variance is known. Since the population variance of 45 is given, and the population is approximately normally distributed, a Z-distribution can be used for estimation. To estimate the population mean μ using the sample mean, we consider the Central Limit Theorem, which tells us that the means of large samples of a population with known variance follow a normal distribution.
An example of constructing a confidence interval given a sample mean of 10 and an error bound of 5 (which defines the 90% confidence interval of (5, 15)) can guide us through the process. The sample mean of 10 is the centre of the interval, and the margin of error, calculated using the Z-score corresponding to the 90% confidence level multiplied by the standard error of the sample mean, defines the range around the sample mean in which we predict the population mean μ lies.
If we were provided with the specific sample mean from our researcher's study, we could apply the same process to estimate the population mean μ with a confidence interval at a 95% confidence level using the standard deviation σ of the square root of 45, and the known Z-score for a 95% confidence level.