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The sampling distribution of the sample mean is the probability distribution of all possible sample means from a population. It describes how the means of different samples will vary and is crucial for understanding the behavior of sample statistics. The Central Limit Theorem states that, regardless of the population's distribution, the sampling distribution will approach a normal distribution as the sample size increases.

The mean of the sampling distribution of the sample means, also known as the expected value, is equal to the population mean (mu). This means that if you take many samples and calculate their means, the average of those means will converge to the population mean. In this case, with mu = 150, the mean of the sampling distribution will also be 150.

The standard deviation of the sampling distribution, often referred to as the standard error, measures the variability of sample means around the population mean. It is calculated by dividing the population standard deviation (sigma) by the square root of the sample size (n). For this problem, with sigma = 25 and n = 49, the standard error can be computed to understand how much sample means will typically deviate from the population mean.