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Since the sample size n=100 is statistically considered to be large (n>30), we assume that the mean of the sampling distribution of x̄ is equal to the population mean, μ.
𝜇𝑥̅ = μ = 55
Also, we estimate the sample standard deviation (𝜎𝑥̅.) using the formula:
where = population standard deviation
Given n=100 and = 20
𝜎𝑥̅ = = = 2
Answer: The sampling distribution of the sample means has 𝜇𝑥̅ = 55 and 𝜎𝑥̅ =2