Final answer:
The standard deviation of the sample mean, under approximately normal conditions, is calculated using the formula σ/√n, which is the population standard deviation divided by the square root of the sample size.
Step-by-step explanation:
If the conditions are met where the sample mean will be approximately normal, the standard deviation of the sample mean, also known as the standard error of the mean, is calculated as σ/√n, where σ is the population standard deviation and n is the sample size. This is option (a), which means the correct formula for the standard deviation of the sample mean, when the Central Limit Theorem applies, is Standard Deviation: σ/√n. This is because as the sample size increases, the distribution of the sample means tends to be approximately normal, regardless of the shape of the original population's distribution.
The mean of these sample means will equal the population mean (μ), and the standard deviation, known as the standard error, will be σ/√n. This effect is due to the Central Limit Theorem, which allows us to approximate the distribution of sample means using the normal distribution for sufficiently large samples. When comparing the sample mean and sample standard deviation to the theoretical mean and theoretical standard deviation, they should align closely if the sample size is large enough.