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Answer :
Final answer:
The mean of the distribution of sample means is 216.3 and the standard deviation of the distribution (also known as the standard error) is about 13.85.
Explanation:
In statistics, for a population with a normal distribution with mean (μ) and standard deviation (σ), we can find the mean and the standard deviation of the distribution of sample means for a given sample size (n).
The mean of the distribution of sample means is equal to the mean of the population. Hence, the mean of the sample means for your population is the same as the given μ, which is 216.3.
The standard deviation of the distribution of sample means, also known as the standard error, is calculated as σ/√n. In this case, σ = 99.1 and n = 51. Therefore, the standard deviation of the distribution of sample means is 99.1/√51 ≈ 13.85 (accurate to two decimal places).
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