The correct answer is C. μ = 15.02, σ = 1.49 . Since both samples are stated to come from the same stable process , the best population estimates should come from the combined information , with greater influence naturally coming from the larger sample . In CSSBB statistics, the sample mean and sample standard deviation are used as estimates of the population parameters when the true values are unknown. Because Sample 2 has a much larger sample size ( 45 versus 12 ), its estimates are more influential and more reliable as point estimates of the process.

If the two samples are combined, the weighted mean is approximately 15.01 , which rounds to 15.02 . The combined standard deviation is approximately 1.49 . Therefore, among the available answer choices, C is the best estimate of the population mean and standard deviation.

The smaller sample should not dominate the estimate when a larger sample from the same stable process is available. Option D is incorrect because 1.57 is not supported by the sample information. Options A and B use the smaller sample mean of 14.98, which is less representative than the estimate supported by the combined data and larger sample.

There is also a correction needed in the option text :

Option D should read σ = 1.57 , not n = 1.57 .