Final answer:
The critical value for a 92% confidence interval with a known population standard deviation and a large sample size (n=25) can be found using the standard normal distribution, which is approximately 1.75.
Step-by-step explanation:
To find the critical value for a 92% confidence interval when the population standard deviation (σ) is known, you would use the standard normal (Z) distribution since the sample size (n) is 25, which is generally considered large enough to approximate the normal distribution.
For a confidence level of 92%, you want to find the Z-score that leaves 4% in the two tails of the standard normal distribution (as 100% - 92% = 8%, and 8%/2 = 4% for each tail). Consulting a Z-table or using a statistical calculator or software, you would look for the Z-score that corresponds to an area of 0.9600 (because 0.5000 + 0.4600 = 0.9600) to the left of it. This Z-score is the critical value.
Typically, the Z-score for a 92% confidence interval is approximately 1.75. With this critical value, you could construct your confidence interval for the population mean.