Stat normal population question?

Question

A sample of 25 outcomes is taken from a population that is Normal(50, 3). The mean of this particular sample is found to be 48.5. What is the probability that a particular sample of the same size (n = 25) from this population would find < 48.5?

Answer 1

You can answer this question using the sampling distribution. According to the central limit theorem, the sampling distribution with N=25 will have a mean of 50 and a sd (i.e., standard error) of .6 (3/sqrt of 25). On this sampling distribution 48.5 is a z-score of -2.5. The area lower than a z-score of -2.5 is about .62%. This is the answer to your question. 

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