The mean of the distribution of sample means for samples of size 25 is <u>μₓ = μ = 14</u>.
The central limit theorem implies that the distribution of the sample means will be roughly normally distributed if you have a population with mean μ and standard deviation σ and take sufficiently enough random samples from the population with replacement. This holds as long as the sample size is sufficient (often n > 30), regardless of whether the source population is normal or skewed. The Theorem is valid even for samples less than 30 if the population is normal.
Using the population's random samples as a source, we may calculate:
The mean of the sample means μₓ = μ, and
the standard deviation of the sample means σₓ = σ/√n.
In the question, the population is normally distributed. Thus, we can use the central limit theorem, which gives that the mean of the sample means: μₓ = μ, making the mean of the distribution of sample means for samples of size 25 = μ = 14.
Thus, the mean of the distribution of sample means for samples of size 25 is <u>μₓ = μ = 14</u>.
Learn more about the central limit theorem at
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