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Probability and Samples

I have a random sample of n = 16 scores with a normal distribution, mean of 50 and standard deviation of 10. I need to calculate what range of values has a 95% probability of containing the sample mean.

Here is where I get stuck. I have been provided the answer and it is 45.13 to 54.87 (50 +/- 4.87). I don't know how to get there. To me, 1/2 of the scores I am looking for are above the mean (50) and 1/2 are below. 1/2 of 95% is 47.5. On the z-score chart under "d" .4750 provides a z-score of 1.96. I have already calculated the standard error as 2.5. 1.96(2.5) = 4.9, so the answer would be 50 +/- 4.9.

I don't know what I am missing.

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