Final answer:
The question pertains to constructing a 90% confidence interval for the population mean using a known standard deviation and a sample mean. This requires utilizing the z-distribution, but the calculation cannot be completed without specific values for the standard deviation and z-score.
Step-by-step explanation:
The subject of this question is related to constructing a confidence interval for a population mean, which is a concept in statistics, a branch of Mathematics. The question appears to fit the College level, as it involves statistical inference which is typically covered at this academic stage.
To construct a 90% confidence interval for the population mean when the population standard deviation is known, one would usually use the z-distribution. The formula to calculate a confidence interval is:
CI = µ ± (z * (σ / √n))
Where µ is the sample mean, z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.
Without the specific standard deviation and z-score values, we cannot complete the calculation. However, assuming we had this information, we'd plug these values into the formula to calculate the error bounds and determine the range of values that the true population mean is likely to fall within. The confidence interval provides an estimate of the population mean with a certain level of confidence, in this case, 90%.