Final answer:
Option (B), The sampling distribution of the sample mean is normally distributed with a mean of 125 mg/dl and a standard deviation of 5 mg/dl.
Step-by-step explanation:
When considering a sampling distribution of the sample mean with a population mean (μ) of 125 mg/dl and a standard deviation (σ) of 10 mg/dl, with a sample size (n) of 4, we apply the central limit theorem. The central limit theorem tells us that, as the sample size becomes larger, the sampling distribution of the sample mean will tend to be normally distributed regardless of the shape of the population distribution.
Since we are dealing with a population that is already normally distributed and taking samples of n=4, we can expect to see the sampling distribution of the sample means also normally distributed.
The mean of the sampling distribution of the sample mean will be the same as the population mean, which is 125 mg/dl. However, the standard deviation of the sampling distribution, often referred to as the standard error (SE), will be the population standard deviation divided by the square root of the sample size.
Therefore, the standard deviation of the sampling distribution will be σ/√n = 10/√4 = 10/2 = 5.
Hence, the correct answer is: Normal, μ=125, σ=5