A population has mean =μ35 and standard deviation =σ5. Find μx and σx for samples of size =n25. Round your answers to one decimal place if needed.μx= σx=
Question
A population has mean =μ35 and standard deviation =σ5. Find μx and σx for samples of size =n25. Round your answers to one decimal place if needed.μx= σx=
Solution
The mean and standard deviation of a sampling distribution are related to the mean and standard deviation of the population from which the samples are drawn.
The mean of the sampling distribution (μx) is equal to the mean of the population (μ). So, μx = μ = 35.
The standard deviation of the sampling distribution (σx), also known as the standard error, is equal to the standard deviation of the population (σ) divided by the square root of the sample size (n). So, σx = σ/√n = 5/√25 = 5/5 = 1.
So, μx = 35 and σx = 1.
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