The mean of the distribution of sample means, based on the parameters, would be 164. 8.
How to find the mean ?
The mean of the distribution of sample means, often referred to as the sampling distribution of the sample mean can be calculated using the same mean (μ) of the population but with a smaller standard deviation (σ/√n) due to the Central Limit Theorem.
The mean of the distribution of sample means for a sample of size 100 from a population with μ = 164.8 and σ = 123.8 is also 164.8.
This is a key result of the Central Limit Theorem, which states that the sampling distribution of the sample mean approaches a normal distribution with the same mean as the population and a standard deviation equal to the population standard deviation divided by the square root of the sample size.